Three-dimensional almost Kenmotsu manifolds satisfying certain nullity conditions

Almost α-Paracosymplectic Manifolds

This paper is a complete study of almost α-paracosmplectic manifolds. We characterize almost α-paracosmplectic manifolds which have para Kaehler leaves. Main curvature identities which are fulfilled by any almost α-paracosmplectic manifold are found. We also proved that ξ is a harmonic vector field if and only if it is an eigen vector field of the Ricci operator. We locally classify three dimensional almost α-para-Kenmotsu manifolds satisfying a certain nullity condition. We show that this condition is invariant under D_{γ,β}-homothetic deformation. Furthermore, we construct examples of almost…

$η$- Ricci Solitons on Kenmotsu manifold with Generalized Symmetric Metric Connection

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.

Metric $f$-contact manifolds satisfying the $(κ,μ)$-nullity condition

We prove that if the $f$-sectional curvature at any point $p$ of a $(2n+s)$-dimensional $f$-$(κ,μ)$ manifold with $n>1$ is independent of the $f$-section at $p$, then it is constant on the manifold. Moreover, we also prove that an $f$-$(κ,μ)$ manifold which is not an $S$-manifold is of constant $f$-sectional curvature if and only if $μ=κ+1$ and we give an explicit expression for the curvature tensor field. Finally, we present some examples.

On contact pseudo-metric manifolds satisfying a nullity condition

In this paper, we aim to introduce and study $(κ, μ)$-contact pseudo-metric manifold and prove that if the $φ$-sectional curvature of any point of $M$ is independent of the choice of $φ$-section at the point, then it is constant on $M$ and accordingly the curvature tensor. Also, we introduce generalized $(κ, μ)$-contact pseudo-metric manifold and prove for $n>1$, that a non-Sasakian generalized $(κ, μ)$-contact pseudo-metric manifold is a $(κ, μ)$-contact pseudo-metric manifold.

Kenmotsu 3-流形上的 η-Ricci 孤子

$η$-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。

para-Kenmotsu流形上的$η$-Ricci孤立子

$η$-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。

On the mean curvature of submanifolds with nullity

In this paper, we investigate geometric conditions for isometric immersions with positive index of relative nullity to be cylinders. There is an abundance of noncylindrical $n$-dimensional minimal submanifolds with index of relative nullity $n-2$, fully described by Dajczer and Florit \cite{DF2} in terms of a certain class of elliptic surfaces. Opposed to this, we prove that nonminimal $n$-dimensional submanifolds in space forms of any codimension are locally cylinders provided that they carry a totally geodesic distribution of rank $n-2\geq2,$ which is contained in the relative nullity distri…

仿切触几何中的 h-几乎 Ricci-Yamabe 孤立子

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。

具有曲率性质的弱几乎${\mathcal S}$-流形的刻画

Characterizations of weak almost ${\mathcal S}$-manifolds with curvature properties

研究弱几乎${\cal S}$-流形在$f$-$(\kappa,\mu)$-零化条件下的曲率性质，利用部分Ricci流刻画${\cal S}$-流形为满足关键性质的弱几乎${\cal S}$-流形的极限，并证明当$\kappa=\mu=0$时的分裂定理。