Li Ma
In this note, we study Q-curvature flow on $S^4$ with indefinite nonlinearity. Our result is that the prescribed Q-curvature problem on $S^4$ has a solution provided the prescribed Q-curvature $f$ has its positive part, which possesses non-degenerate critical points such that $Δ_{S^4} f\not=0$ at the saddle points and an extra condition such as a nontrivial degree counting condition.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
In this paper, we consider the indefinite scalar curvature problem on $R^n$. We propose new conditions on the prescribing scalar curvature function such that the scalar curvature problem on $R^n$ (similarly, on $S^n$) has at least one solution. The key observation in our proof is that we use the bifurcation method to get a large solution and then after establishing the Harnack inequality for solutions near the critical points of the prescribed scalar curvature and taking limit, we find the nontrivial positive solution to the indefinite scalar curvature problem.
We present a compared analysis of some properties of indefinite almost $\mathcal{S}$-manifolds and indefinite $\mathcal{S}$-manifolds. We give some characterizations in terms of the Levi-Civita connection and of the characteristic vector fields. We study the sectional and $ϕ$-sectional curvature of indefinite almost $\mathcal{S}$-manifolds and state an expression of the curvature tensor field for the indefinite $\mathcal{S}$-space forms. We analyse the sectional curvature of indefinite $\mathcal{S}$-manifold in which the number of the spacelike characteristic vector fields is equal to that of …
Some curvature properties of Kahler manifolds of indefinite metrics are studied. Analogues of a Kulkarni's theorem are proved for such manifolds.
Improving a result of Eschenburg and Kim we give a criterion for semisimplicity of pseudo-Riemannian extrinsic symmetric spaces in terms of the shape operator with respect to the mean curvature vector.
We study two types of isotropic planes: weakly isotropic and strongly isotropic planes. We prove that a Riemannian manifold of indefinite metric is conformally flat if and only if its curvature tensor vanishes on all the strongly isotropic planes. We specialize the plane axiom for Riemannian manifolds of indefinite metrics. We show that manifolds satisfying plane axiom of weakly (strongly) isotropic planes are of constant sectional curvature (conformaly flat). Further we study analogous problems on almost Hermitian manifolds of indefinite metrics.
On the curvature symmetries in lightlike hypersurfaces of an indefinite Sasakian manifold
本文研究不定 Sasakian 流形中相切于结构向量场的类光超曲面，证明其不具备局部对称、半对称或半平行等曲率对称性。
We classify the connected pseudo-Riemannian manifolds of signature $(p,q)$ with $q\ge5$ so that at each point of $M$ the skew-symmetric curvature operator has constant rank 2 and constant Jordan normal form on the set of spacelike 2 planes and so that the skew-symmetric curvature operator is not nilpotent for at least one point of $M$.
A submanifold of a pseudo-Riemannian manifold is said to have parallel mean curvature vector if the mean curvature vector field H is parallel as a section of the normal bundle. Submanifolds with parallel mean curvature vector are important since they are critical points of some natural functionals. In this paper, we survey some classical and recent results on submanifolds with parallel mean curvature vector. Special attention is paid to the classification of space-like and Lorentz surfaces with parallel mean curvature vector in Riemannian and indefinite space forms.
We introduce higher order mean curvatures of screen almost conformal (SAC) half-lightlike submanifolds of indefinite contact manifolds, admitting a semi-symmetric non-metric connection, and use them to generalize some known results of [6]. Also, we derive a new set of integration formulae via the divergence of some special vector fields tangent to this submanifold. Several examples are also included to illustrate the main concepts.
We classify those curvature-homogeneous Einstein four-manifolds, of all metric signatures, which have a complex-diagonalizable curvature operator. They all turn out to be locally homogeneous. More precisely, any such manifold must be either locally symmetric or locally isometric to a suitable Lie group with a left-invariant metric. To show this we explicitly determine the possible local-isometry types of manifolds that have the properties named above, but are not locally symmetric.
The Jacobi-orthogonality in indefinite scalar product spaces
本文推广Jacobi正交性至不定内积空间，研究其与Osserman、Jacobi对偶的关系，证明拟Clifford张量Jacobi正交，并给出3维和4维代数曲率张量Jacobi正交的充要条件。
Conditions, related to Kulkarni's equivalence problem are considered for indefinite Riemannian and Kaehlerian manifolds. Corresponding theorems are obtained for the values of the Ricci tensor on isotropic vectors as well as for the values of the curvature tensor on degenerate holomorphic 2-planes.
We study lightlike submanifolds of indefinite statistical manifolds. Contrary to the classical theory of submanifolds of statistical manifolds, lightlike submanifolds of indefinite statistical manifolds need not to be statistical submanifold. Therefore we obtain some conditions for a lightlike submanifold of indefinite statistical manifolds to be a lightlike statistical submanifold. We derive the expression of statistical sectional curvature and finally obtain some conditions for the induced statistical Ricci tensor on a lightlike submanifold of indefinite statistical manifolds to be symmetric…
Parallel Radical and Screen Distributions on Lightlike Hypersurfaces of Indefinite Statistical Manifolds
本文研究不定统计流形光锥超曲面的径向与屏幕分布平行条件，给出基于屏幕形状算子和差分张量的判据，并探讨度量情形下联络与曲率性质。
The indefinite metric of R. Mrugala and the geometry of the thermodynamical phase space
本文研究了均匀热力学系统接触相空间的不定度量，计算了其曲率张量等几何性质，建立了与 Heisenberg Lie 群的同构，并引入了双曲射影化以实现相空间的自然紧致化。
For homogeneous metrics on the spaces of the title it is shown that the Ricci flow can move a metric of stricly positive sectional curvature to one with some negative sectional curvature and one of positive definite Ricci tensor to one with indefinite signature.
In this paper we introduce the concept of $(\varepsilon)$-almost paracontact manifolds, and in particular, of $(\varepsilon)$-para Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci tensor of $(\varepsilon)$-para Sasakian manifolds are obtained. We prove that if a semi-Riemannian manifold is one of flat, proper recurrent or proper Ricci-recurrent, then it can not admit an $(\varepsilon)$-para Sasakian structure. We show that, for an $(\varepsilon)$-para Sasakian manifold, the conditions of being symmetric, semi-symmetric or of constant se…
In this note, we study the curvature flow to Nirenberg problem on $S^2$ with non-negative nonlinearity. This flow was introduced by Brendle and Struwe. Our result is that the Nirenberg problems has a solution provided the prescribed non-negative Gaussian curvature $f$ has its positive part, which possesses non-degenerate critical points such that $Δ_{S^2} f>0$ at the saddle points.
We present two initial graphs over the entire $\mathbb{R}^n$, $n \geq 2$ for which the mean curvature flow behaves differently from the heat flow. In the first example, the two flows stabilize at different heights. With our second example, the mean curvature flow oscillates indefinitely while the heat flow stabilizes. These results highlight the difference between dimensions $n \geq 2$ and dimension $n=1$, where Nara-Taniguchi proved that entire graphs in $C^{2,α}(\mathbb{R})$ evolving under curve shortening flow converge to solutions to the heat equation with the same initial data.
The prescribed Gauduchon scalar curvature problem in almost Hermitian geometry
该研究针对近厄米流形的指定Gauduchon标量曲率问题，通过共形变化推导将其转化为带指数非线性的半线性偏微分方程，用上下解方法证明解的存在性与Gauduchon度相关常数的符号有关，负号时给出充要条件，还复现了三类相关Yamabe问题。
Yamabe type equations with a sign-changing nonlinearity, and the prescribed curvature problem
本文研究非紧黎曼流形上变号函数的预定标量曲率问题，通过标准与共形拉普拉斯算子的谱性质，在极低假设下证明了两个保证拟等距的新存在性结果，并推广至拟线性方程与Schrödinger型算子的次临界理论。
Noncollapsing for Curvature Flows with Inhomogeneous Speeds
本文研究欧氏空间中完全非线性曲率流，在速度函数凸或逆凹及调制函数满足结构条件时，建立外部非坍缩估计，并改进逆凹情形的内部论证。
In this paper we study the 3-dimensional $(\varepsilon) $-para Sasakian manifolds. We obtain an necessary and sufficient condition for an $(\varepsilon ) $-para Sasakian 3 -manifold to be an indefinite space form. We show that a Ricci-semi-symmetric $(\varepsilon) $-para Sasakian 3 -manifold is an indefinite space form. We investigate the necessary and sufficient condition for an $(\varepsilon) $-para Sasakian 3 -manifold to be locally $φ$-symmetric. It is proved that in an $ (\varepsilon) $-para Sasakian 3-manifold with $η$ -parallel Ricci tensor the scalar curvature is constant. It is also s…
Riemannian curvature of gaussian distribution in dual coordinate system
本文研究高斯分布黎曼流形在对偶坐标系下的曲率与挠率，并显式给出Amari公式以刻画对偶势函数和Fisher度量等几何不变量。
In this paper we are interested in defining affine structures on discrete quadrangular surfaces of the affine three-space. We introduce, in a constructive way, two classes of such surfaces, called respectively indefinite and definite surfaces. The underlying meshes for indefinite surfaces are asymptotic nets satisfying a non-degeneracy condition, while the underlying meshes for definite surfaces are non-degenerate conjugate nets satisfying a certain natural condition. In both cases we associate to any of these nets several discrete affine invariant quantities: a metric, a normal and a co-norma…
Rigidity of weighted manifolds via classification results for semilinear equations
本文通过半线性方程的分类结果，研究加权流形的刚性，并证明正解的存在性与流形的刚性及权重的平凡性之间的关系。
Spacelike Brakke flows with boundary in pseudo-Euclidean space
研究伪欧几里得空间中带边界的类空平均曲率流，通过建立弱形式、引入相关向量，证明闭包和紧致性定理等，采用椭圆正则化程序证明存在性，为研究奇点外的弱类空平均曲率流提供变差设置。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。