Soumendu Roy, Santu Dey, Arindam Bhattacharyya
The object of the present paper is to study some properties of Kenmotsu manifold whose metric is conformal $η$-Einstein soliton. We have studied some certain properties of Kenmotsu manifold admitting conformal $η$-Einstein soliton. We have also constructed a 3-dimensional Kenmotsu manifold satisfying conformal $η$-Einstein soliton.
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The aim of this article is to study the Riemann soliton and gradient almost Riemann soliton on certain class of almost Kenmotsu manifolds. Also some suitable examples of Kenmotsu and $(κ,μ)'$-almost Kenmotsu manifolds are constructed to justify our results.
The goal of our present paper is to deliberate $*$-conformal $η$-Ricci soliton within the framework of Kenmotsu manifolds. Here we have shown that a Kenmotsu metric as a $*$-conformal $η$-Ricci soliton is Einstein metric if the soliton vector field is contact. Further, we have evolved the characterization of the Kenmotsu manifold or the nature of the potential vector field when the manifold satisfies gradient almost $*$-conformal $η$-Ricci soliton. Next, we have contrived $*$-conformal $η$-Ricci soliton admitting $(κ,μ)^\prime$-almost Kenmotsu manifold and proved that the manifold is Ricci fla…
In this short note it is established that there does not exist Ricci soliton with the Reeb potential vector field in an almost Kenmotsu manifold (briefly, $\mathcal{AKM}$).
In this paper the notion of Ricci $ρ$-soliton as a generalization of Ricci soliton is defined. We are motivated by the Ricci-Bourguignon flow to define this concept. We show that if a 3- dimensional almost Kenmotsu Einstein manifold $M$ be a $ρ$-soliton, then $M$ is a Kenmotsu manifold of constant sectional curvature $-1$ and the $ρ$-soliton is expanding, with $λ=2$.
Characterizations of $\ast$-Ricci-Bourguignon solitons on Kenmotsu manifolds
本文研究了Kenmotsu流形上* -Ricci-Bourguignon溶iton的特征，探讨了其压缩、平衡和扩大的条件，以及与tors-forming向量场的关系，并给出了一个5维例子。
Solitonic aspects of submanifolds in Kenmotsu statistical manifolds
本文研究Kenmotsu统计流形及其子流形上的统计孤子、Yamabe孤子及几乎拟Yamabe孤子，探讨其统计曲率性质，并给出5维示例。主要贡献在于系统分析这些孤子在共圆与共点向量场下的行为。
The Eisenhart problem of finding parallel tensors is solved for the symmetric case in the regular $f$-Kenmotsu framework. On this way, the Olszack-Rosca example of Einstein manifolds provided by $f$-Kenmotsu manifolds via locally symmetric Ricci tensors is recovered as well as a case of Killing vector fields. Some other classes of Einstein-Kenmotsu manifolds are presented. Our result is interpreted in terms of Ricci solitons and special quadratic first integrals.
In this paper we characterize the Einstein metrics in such broader classes of metrics as almost $η$-Ricci solitons and $η$-Ricci solitons on Kenmotsu manifolds, and generalize some results of other authors. First, we prove that a Kenmotsu metric as an $η$-Ricci soliton is Einstein metric if either it is $η$-Einstein or the potential vector field $V$ is an infinitesimal contact transformation or $V$ is collinear to the Reeb vector field. Further, we prove that if a Kenmotsu manifold admits a gradient almost $η$-Ricci soliton with a Reeb vector field leaving the scalar curvature invariant, then …
The object of the present paper is to characterize two classes of almost Kenmotsu manifolds admitting Ricci-Yamabe soliton. It is shown that a $(k,μ)'$-almost Kenmotsu manifold admitting a Ricci-Yamabe soliton or gradient Ricci-Yamabe soliton is locally isometric to the Riemannian product $\mathbb{H}^{n+1}(-4) \times \mathbb{R}^n$. For the later case, the potential vector field is pointwise collinear with the Reeb vector field. Also, a $(k,μ)$-almost Kenmotsu manifold admitting certain Ricci-Yamabe soliton with the curvature property $Q \cdot P = 0$ is locally isometric to the hyperbolic space…
In the present paper, we characterize a class of almost Kenmotsu manifolds admitting quasi Yamabe soliton. It is shown that if a $(k,μ)'$-almost Kenmotsu manifold admits a quasi Yamabe soliton $(g,V,λ,α)$ with $V$ pointwise collinear with $ξ$, then (1) $V$ is a constant multiple of $ξ$, (2) $V$ is a strict infinitesimal contact transformation and (3) $(£_V h')X = 0$ for any vector field $X$. Finally an illustrative example is presented to support the result.
In this paper, we consider the notion of Cotton soliton within the framework of almost Kenmotsu 3-$h$-manifolds. First we consider that the potential vector field is pointwise collinear with the Reeb vector field and prove a non-existence of such Cotton soliton. Next we assume that the potential vector field is orthogonal to the Reeb vector field. It is proved that such a Cotton soliton on a non-Kenmotsu almost Kenmotsu 3-$h$-manifold such that the Reeb vector field is an eigen vector of the Ricci operator is steady and the manifold is locally isometric to $\mathbb{H}^2(-4) \times \mathbb{R}$.
This manuscript examines almost Kenmotsu manifolds (briefly, AKMs) endowed with the almost Ricci-Yamabe solitons (ARYSs) and gradient ARYSs. The condition for an AKM with ARYS to be $η$-Einstein is established. We also show that an ARYS on Kenmotsu manifold becomes Ricci-Yamabe soliton under certain restrictions. In this series, it is proven that a $(2n+1)$-dimensional $(κ, μ)'$-AKM equipped with a gradient ARYS is either locally isometric to $\mathbb{H}^{n+1}(-4)\times\mathbb{R}^n$ or the Reeb vector field and the soliton vector field are codirectional. The properties of $3$-dimensional non-K…
Geometry of $*$-$k$-Ricci-Yamabe soliton and gradient $*$-$k$-Ricci-Yamabe soliton on Kenmotsu manifolds
该文在Kenmotsu流形框架下研究$*$-$k$-Ricci-Yamabe孤立子的几何性质，推导标量曲率、向量场刻画及相关应用，结合梯度$*$-$η$-Einstein孤立子分析黎曼曲率张量，并构造5维实例验证结论。
Existence, Stability, and Geometric Implications of $\ast$-$η$-Schouten Solitons on Kenmotsu Manifolds
本文研究Kenmotsu流形上当势向量场为torsion-forming时$\ast$-$\eta$-Schouten孤子的刻画，推导标量曲率，讨论向量场的性质，并考察无穷小CL变换和Schouten-Van Kampen联络，最后构造三维例子验证结果。
Geometric solitons in a $D$-homothetically deformed Kenmotsu manifold
该文研究$D$-同伦形变Kenmotsu流形中三类势向量场对应的近Riemann与近Ricci孤立子，推导部分情形的曲率表达式，并给出形变流形含梯度孤立子时初始流形Ricci曲率的下界。
$η$-Ricci Solitons on Kenmotsu 3-Manifolds
本文研究 Kenmotsu 3-流形上的 η-Ricci 孤子，涵盖 Codazzi 型 Ricci 张量、循环平行 Ricci 张量、ϕ-Ricci 对称性及曲率条件 R.R=Q(S,R)，并通过构造例子证明适当 η-Ricci 孤子的存在性。
A note on gradient Solitons on two classes of almost Kenmotsu Manifolds
该研究在两类近Kenmotsu流形框架下刻画梯度$(m,ρ)$-拟爱因斯坦孤立子，并借助实例验证相关结果，丰富了近Kenmotsu流形上梯度孤立子的研究内容。
The objective of the present paper is to study the $η$-Ricci solitons on Kenmotsu manifold with generalized symmetric metric connection of type $(α,β)$. There are discussed Ricci and $η$-Ricci solitons with generalized symmetric metric connection of type $(α,β)$ satisfying the conditions $\bar{R}.\bar{S}=0$, $\bar{S}.\bar{R}=0$, $\bar{W_{2}}.\bar{S}=0$ and $\bar{S}.\bar{W_{2}}=0.$. Finally, we construct an example of Kenmotsu manifold with generalized symmetric metric connection of type $(α,β)$ admitting $η$-Ricci solitons.
In this paper, we consider $*$-Ricci soliton in the frame-work of Kenmotsu manifolds. First, we prove that if the metric of a Kenmotsu manifold $M$ is a $*$-Ricci soliton, then soliton constant $λ$ is zero. For 3-dimensional case, if $M$ admits a $*$-Ricci soliton, then we show that $M$ is of constant sectional curvature -1. Next, we show that if $M$ admits a $*$-Ricci soliton whose potential vector field is collinear with the characteristic vector field $ξ$, then $M$ is Einstein and soliton vector field is equal to $ξ$. Finally, we prove that if $g$ is a gradient almost $*$-Ricci soliton, the…
CR-hypersurfaces of conformal Kenmotsu space form satisfying certain shape operator conditions
Kenmotsu Contact Geometry Through the Lens of $\ast-\boldsymbolκ$-Ricci-Bourguignon Almost Solitons
研究 Kenmotsu 流形上 $\ast-\boldsymbol{\kappa}$-Ricci-Bourguignon 几乎孤子的性质，推导标量曲率，构造向量场，并探索扭形向量场的应用，给出五维实例。
In this paper, we investigate the condition on warped product manifold of a Kenmotsu manifold and the real line to be a conformal Kahler manifold. This result demonstrates the close relation of Kenmotsu and Kahler manifolds.
In this paper, a systematic study of Kenmotsu pseudo-metric manifolds are introduced. After studying the properties of this manifolds, we provide necessary and sufficient condition for Kenmotsu pseudo-metric manifold to have constant $φ$-sectional curvature, and prove the structure theorem for $ξ$-conformally flat and $φ$-conformally flat Kenmotsu pseudo-metric manifolds. Next, we consider Ricci solitons on this manifolds. In particular, we prove that an $η$-Einstein Kenmotsu pseudo-metric manifold of dimension higher than 3 admitting a Ricci soliton is Einstein, and a Kenmotsu pseudo-metric 3…
$\ast$-$η$-Ricci solitons and Einstein metrics on a weak $β$-Kenmotsu manifold
本文在弱$\beta$-Kenmotsu流形上引入$\ast$-Ricci张量，研究$\ast$-$\eta$-Ricci孤立子与结构（$\beta$为常数）的相互作用，得到Einstein度量的新特征。
$η$-Ricci solitons on para-Kenmotsu manifolds
本文在仿切触几何背景下研究满足特定曲率条件的para-Kenmotsu流形上的$η$-Ricci孤立子，证明其存在蕴含流形拟爱因斯坦，满足特定曲率条件时为爱因斯坦流形，并给出其存在的充分条件。
$\ast$-$η$-Ricci solitons on weak Kenmotsu $f$-manifolds
本文将 *-Ricci 张量引入弱度量 f-流形，研究 *-η-Ricci 孤立子与弱 βf-Kenmotsu 结构的相互作用，并给出 η-Einstein 度量的新特征。
$η$-Ricci solitons and $η$-Einstein metrics on weak $β$-Kenmotsu $f$-manifolds
本文研究弱$β$-Kenmotsu $f$-流形，证明其局部为扭曲积，并得出满足条件的$η$-Ricci孤立子结构使流形成为常数量曲率的$η$-Einstein流形。
The object of the present paper is to characterize the class of Kenmotsu manifolds which admits conformal $η$-Ricci soliton. Here, we have investigated the nature of the conformal $η$-Ricci soliton within the framework of Kenmotsu manifolds. It is shown that an $η$-Einstein Kenmotsu manifold admitting conformal $η$-Ricci soliton is an Einstein one. Moving further, we have considered gradient conformal $η$-Ricci soliton on Kenmotsu manifold and established a relation between the potential vector field and the Reeb vector field. Next, it is proved that under certain condition, a conformal $η$-Ri…
Conformal vector fields on almost Kenmotsu manifolds
本文研究几乎Kenmotsu流形上的共形向量场，推导两类共形向量场情形下流形的结构与扭曲积形式，证明带Killing向量场的$(k,μ)'$-几乎Kenmotsu流形的两种结构，还研究了其上的η-Ricci-Yamabe孤立子并构造实例。
A Willmore surface $y:M\rightarrow S^{n+2}$ has a natural harmonic oriented conformal Gauss map $Gr_y:M\rightarrow SO^{+}(1,n+3)/SO(1,3)\times SO(n)$, which maps each point $p\in M$ to its oriented mean curvature 2-sphere at $p$. An easy observation shows that all conformal Gauss maps of Willmore surfaces satisfy a restricted nilpotency condition which will be called "strongly conformally harmonic." The goal of this paper is to characterize those strongly conformally harmonic maps from a Riemann surface $M$ to $SO^+ (1, n + 3)/{SO^+(1, 3) \times SO(n) }$ which are the conformal Gauss maps of s…
In the present paper, we give some characterizations by considering $*$-Ricci soliton as a Kenmotsu metric. We prove that if a Kenmotsu manifold represents an almost $*$-Ricci soliton with the potential vector field $V$ is a Jacobi along the Reeb vector field, then it is a steady $*$-Ricci soliton. Next, we show that a Kenmotsu matric endowed an almost $*$-Ricci soliton is Einstein metric if it is $η$-Einstein or the potential vector field $V$ is collinear to the Reeb vector field or $V$ is an infinitesimal contact transformation.
In this paper we study para-Kenmotsu manifolds. We characterize this manifolds by tensor equations and study their properties. We are devoted to a study of $η-$Einstein manifolds. We show that a conformally flat para-Kenmotsu manifold is a space of constant negative curvature $-1$ and we prove that if a para-Kenmotsu manifold is a space of constant $φ-$para-holomorphic sectional curvature $H$, then it is a space of constant curvature and $H=-1$. Finally the object of the present paper is to study a 3-dimensional para-Kenmotsu manifold, satisfying certain curvature conditions. Among other, it i…
The purpose of this paper is to study anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds. Several fundamental results in this respect are proved. The integrability of the distributions and the geometry of foliations are investigated. We proved that there do not exist (anti-invariant) Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds such that characteristic vector field ξ is a vertical vector field. We gave a method to get horizontally conformal submersion examples from warped product manifolds onto Riemannian manifolds. Furthermore, …
H-almost Ricci-Yamabe solitons in paracontact geometry
本文在仿切触几何框架下分类了 h-几乎 Ricci-Yamabe 孤立子，系统刻画了 para-Kenmotsu、para-Sasakian 和 para-cosymplectic 流形上的相关结构，并给出两个实例加以说明。
In the present paper, we characterize almost Kenmotsu manifolds admitting holomorphically planar conformal vector (HPCV) fields. We have shown that if an almost Kenmotsu manifold $M^{2n+1}$ admits a non-zero HPCV field $V$ such that $ϕV = 0$, then $M^{2n+1}$ is locally a warped product of an almost Kaehler manifold and an open interval. As a corollary of this we obtain few classifications of an almost Kenmotsu manifold to be a Kenmotsu manifold and also prove that the integral manifolds of D are totally umbilical submanifolds of $M^{2n+1}$. Further, we prove that if an almost Kenmotsu manifold…
The purpose of the paper is to study Yamabe solitons on three-dimensional para-Sasakian, paracosymplectic and para-Kenmotsu manifolds. Mainly, we proved that *If the semi-Riemannian metric of a three-dimensional para-Sasakian manifold is a Yamabe soliton, then it is of constant scalar curvature, and the flow vector field V is Killing. In the next step, we proved that either manifold has constant curvature -1 and reduces to an Einstein manifold, or V is an infinitesimal automorphism of the paracontact metric structure on the manifold. *If the semi-Riemannian metric of a three-dimensional paraco…
A Weierstrass-Kenmotsu Type Representation for CMC $0\le H<1$ in \$\mathbb{H}^3(-1)$
本文提出一种Weierstrass-Kenmotsu型表示，用于描述常均曲率$0\le H<1$的浸入，结合Hermitian模型、平衡谱变形和Iwasawa分解，建立局部浸入与复参数λ的关系，并探讨其与Aiyama和Akutagawa表示的对应关系。
In this paper, we study conformal Ricci solitons and conformal gradient Ricci solitons on generalized ($κ,μ$)-space forms. The conditions for the solitons to be shrinking, steady, and expanding are derived in terms of conformal pressure p. We show under what conditions a Ricci semi-symmetric generalized ($κ,μ$)-space form equipped with a conformal Ricci soliton forms an Einstein manifold.
In this paper, we initiate the study of conformal $η$-Ricci soliton and almost conformal $η$-Ricci soliton within the framework of para-Sasakian manifold. We prove that if para-Sasakian metric admits conformal $η$-Ricci soliton, then the manifold is $η$-Einstein and either the soliton vector field $V$ is Killing or it leaves $ϕ$ invariant. Here, we have shown the characteristics of the soliton vector field $V$ and scalar curvature when the manifold admitting conformal $η$-Ricci soliton and vector field is pointwise collinear with the characteristic vector field $ξ$. Next, we show that a para-S…
The goal of this paper is to study conformal Yamabe soliton and $*$-Yamabe soliton, whose potential vector field is torse forming. Here, we have characterized conformal Yamabe soliton admitting potential vector field as torse forming with respect to Riemannian connection, semi-symmetric metric connection and projective semi-symmetric connection on Riemannian manifold. We have also shown the nature of $*$-Yamabe soliton with torse forming vector field on Riemannian manifold admitting Riemannian connection. Lastly we have developed an example to corroborate some theorems regarding Riemannian con…
The object of the present paper is to study some properties of para-K$ä$hler manifold whose metric is conformal Einstein soliton. We have studied some certain curvature properties of para-K$ä$hler manifold admitting conformal Einstein soliton.
In this paper we study *-Conformal η-Ricci soliton on Sasakian manifolds. Here, we discuss some curvature properties on Sasakian manifold admitting *-Conformal η-Ricci soliton. We obtain some significant results on *-Conformal η-Ricci soliton in Sasakian manifolds satisfying R(ξ,X).S = 0, S(ξ,X).R = 0, {\overline}P(ξ,X).S = 0, where {\overline}P is Pseudo-projective curvature tensor.The conditions for *-Conformal η-Ricci soliton on Φ-conharmonically flat and Φ-projectively flat Sasakian manifolds have been obtained in this article. Lastly we give an example of 5-dimensional Sasakian manifolds …
We investigate Kähler metrics conformal to gradient Ricci solitons, and base metrics of warped product gradient Ricci solitons. The latter we name quasi-solitons. A main assumption that is employed is functional dependence of the soliton potential, with the conformal factor in the first case, and with the warping function in the second. The main result in the first case is a partial classification in dimension $n\geq 4$. In the second case, Kähler quasi-soliton metrics satisfying the above main assumption are shown to be, under an additional genericity hypothesis, necessarily Riemannian produc…
The present paper is to deliberate the geometric composition of a perfect fluid spacetime with torse-forming vector field ξ in connection with conformal Ricci-Yamabe metric and conformal η-Ricci-Yamabe metric. Here we have delineated the conditions for conformal Ricci-Yamabe soliton to be expanding, steady, or shrinking. Later, we have acquired Laplace equation from conformal η-Ricci-Yamabe soliton equation when the potential vector field ξ of the soliton is of gradient type. Lastly, we have designated perfect fluid with Robertson-Walker spacetime and some applications of physics and gravity.
Clairaut conformal submersions from Ricci solitons
本文研究全流形带Ricci孤立子的Clairaut共形淹没，推导了纤维、底流形的相关曲率条件，给出向量场性质的判据及调和淹没的充要条件，并提供非平凡实例。
In this paper, we completely classify conformal solitons on pseudo-Riemannian hypersurfaces in pseudo-Euclidean spaces arisen from the position vector field. In particular, the classification of Yamabe solitons on pseudo-Riemannian hypersurfaces in pseudo-Euclidean spaces arisen from the position vector field can be obtained.
In this paper we extend some well-known rigidity results for conformal changes of Einstein metrics to the class of generalized quasi-Einstein (GQE) metrics, which includes gradient Ricci solitons. In order to do so, we introduce the notions of conformal diffeomorphisms and vector fields that preserve a GQE structure. We show that a complete GQE metric admits a structure-preserving, non-homothetic complete conformal vector field if and only if it is a round sphere. We also classify the structure-preserving conformal diffeomorphisms. In the compact case, if a GQE metric admits a structure-preser…
On conformal collineation and almost Ricci solitons
该研究在微分几何领域，给出了带非平凡闭仿射共形Killing向量场的黎曼流形等距于欧氏球面或欧氏空间的条件，并推导了带仿射共形Killing势向量场的近Ricci孤立子的平凡性结果。
The aim of this paper is characterize a class of contact metric manifolds admitting $\ast$-conformal Ricci soliton. It is shown that if a $(2n + 1)$-dimensional $N(k)$-contact metric manifold $M$ admits $\ast$-conformal Ricci soliton or $\ast$-conformal gradient Ricci soliton, then the manifold M is $\ast$-Ricci at and locally isometric to the Riemannian of a flat $(n + 1)$-dimensional manifold and an $n$-dimensional manifold of constant curvature 4 for $n > 1$ and flat for $n = 1$. Further, for the first case, the soliton vector field is conformal and for the $\ast$-gradient case, the potenti…
$\ast$-conformal Einstein solitons on N(k)-contact metric manifolds
本文研究 N(k)-切触度量流形上 *-共形爱因斯坦孤子及梯度型孤子，刻画了流形性质、势向量场与势函数，给出扩张、稳定和收缩条件，并用例子验证结论。
The aim of this paper is to introduce a notion of mean curvature flow soliton general enough to encompass target spaces of constant sectional curvature, Riemannian products or, in increasing generality, warped product spaces.
In this paper we prove that any complete conformal gradient soliton with nonnegative Ricci tensor is either isometric to a direct product $\mathbb{R}\times N^{n-1}$, or globally conformally equivalent to the Euclidean space $\mathbb{R}^{n}$ or to the round sphere $\mathbb{S}^{n}$. In particular, we show that any complete, noncompact, gradient Yamabe-type soliton with positive Ricci tensor is rotationally symmetric, whenever the potential function is nonconstant.
We show that a complete gradient Ricci soliton $(M^n,\,g)$ with constant scalar curvature and a non-parallel closed conformal vector field is isometric to either the Euclidean space, or an Euclidean sphere, or negatively Einstein warped product of the real line with a complete non-positively Einstein manifold. Moreover, we show that a Kähler gradient Ricci soliton of real dimension $\ge 4$, with a non-parallel closed conformal real vector field is Ricci-flat (Calabi-Yau) and is flat in dimension 4. Finally, we show that a Ricci soliton whose associated 1-form is harmonic, has constant scalar c…
In this paper we introduce, in the Riemannian setting, the notion of conformal Ricci soliton, which includes as particular cases Einstein manifolds, conformal Einstein manifolds and (generic and gradient) Ricci solitons. We provide here some necessary integrability conditions for the existence of these structures that also recover, in the corresponding contexts, those already known in the literature for conformally Einstein manifolds and for gradient Ricci solitons. A crucial tool in our analysis is the construction of some appropriate and highly nontrivial $(0,3)$-tensors related to the geome…
Conformal Submersions Whose Total Manifolds Admit a Ricci Soliton
本文研究全流形为Ricci孤立子的共形淹没，推导O'Neill张量性质、全测地充要条件、Ricci张量与标量曲率公式，得到纤维和底流形的相关几何结构必要条件及调和映射充要条件。
Let $\overline{M}^{n+1}$ be a semi-Riemannian manifold of constant sectional curvature, and endowed with a conformal vector field . Consider a Riemannian manifold $M^n$, isometrically immersed into $\overline{M}^{n+1}$. With these hypotheses in mind, the ultimate goal of this paper is to investigate the intimate relationship between conformal vector fields on $\overline{M}^{n+1}$ and the Ricci almost soliton structure on $M^n$. Assuming that the latter manifold is connected and totally umbilic, we prove that it is naturally given a Ricci almost soliton structure by means of the tangential part…
In this paper we show that all conformal metrics to a pseudo-euclidean space invariant under the translation group, and all the conformal metrics product manifold also invariant by translation where F m it is Ricci flat semi-Riemannian manifold, are gradient Ricci almost soliton. We also proved that all conformal metrics to a euclidean space and invariant by rotation are gradient Ricci almost soliton.
Yamabe solitons on conformal Sasaki-like almost contact B-metric manifolds
本文在近切触B度量流形上通过切触共形变换定义Yamabe孤子，研究余切触与Sasaki类情形，并给出5维李群实例。
Gradient estimates for positive eigenfunctions of $ \mathcal{L} $-operator on conformal solitons and its applications
本文在由一般共形向量场给出的共形孤立子上证明 $\mathcal{L}$-算子正特征函数的局部梯度估计，并由此得到改进的 Liouville 型定理，且在自收缩子情形下获得更优结果。
The purpose of this paper is to study gradient $k$-Yamabe solitons conformal to pseudo-Euclidean space. We characterize all such solitons invariant under the action of an $(n-1)$-dimensional translation group. For rotational invariant solutions, we provide the classification of solitons with null curvatures. As an application, we construct infinitely many explicit examples of geodesically complete steady gradient $k$-Yamabe solitons conformal to the Lorentzian space.
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