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conformally flat AFFINE HYPERSURFACES WITH SEMI-PARALLEL CUBIC FORM

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Acta Mathematica Scientia 2023年第6期43卷 2413-2429页

作者：徐辉阳李策策 School of Mathematics and Statistics Henan University of Science and TechnologyLuoyang 471023China

In this paper,we study locally strongly convex affine hypersurfaces with the vanishing Weyl curvature tensor and semi-parallel cubic form relative to the Levi-Civita connection of the affine *** a main result,we classify these hypersurfaces as not being of a flat affine *** particular,2 and 3-dimensional locally strongly convex affine hypersurfaces with semi-parallel cubic forms are completely determined.

关键词： affine hypersurface semi-parallel cubic form Levi-Civita connection conformally flat warped product

On Submanifolds in Locally Symmetric and conformally flat Riemannian Manifolds

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Journal of Beijing Institute of Technology 2005年第2期14卷 208-211页

作者：孙华飞汤莉陈春 School of Science Beijing Institute of Technology Beijing100081 China School

Let N n+p be an (n+p)-dimensional locally symmetric and conformally flat Riemannian manifold and Mn be an n-dimensional compact submanifold minimally immersed in N n+p . Instead of (n+p)-dimensional unit sphere, we generalize Pinching Theorems about submanifolds in unit sphere and get theorems about submanifolds in locally symmetric and conformally flat Riemannian manifold.

关键词： locally symmetric conformally flat minimal submanifold

The Minimal Submanifolds in a Locally Symmetric and conformally flat Riemannian Manifold

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Chinese Quarterly Journal of Mathematics 1993年第4期8卷 71-76页

作者：舒世昌 Dept.of Math.Xianyang Teacher's Colleage Shanxi712000

In this paper,we extend two important theorem in[1],[2]to the minimal submanifolds in a Locally symmetric and conformally flat Riemannian mainfold N^(+p).When N^(+p)is a space S_(1)^(+p) of constant curvature,our theo... 详细信息

关键词： Locally symmetric conformally flat minimal submanifold

The Submanifolds with Parallel Mean Curvature Vector in a Locally Symmetric and conformally flat Riemannian Manifold

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Chinese Quarterly Journal of Mathematics 1992年第1期7卷 32-36页

作者：孙华飞东北工学院数学系沈阳110006

In the present paper we obtain the following result: Theorem Let M^R be a compact submanifold with parallel mean curvature vector in a locally symmetric and conformally flat Riemannian manifold N^(n+p)(p>1). If then M... 详细信息

关键词： Locally symmetric conformally flat parallel mean curvature vector

Gap Theorem on Complete Noncompact Riemannian Manifold

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Journal of Mathematical Research and Exposition 2011年第3期31卷 429-436页

作者： Cheng Bing ZHAO1,2 1.Department of Mathematics,Anhui University of Architecture,Anhui 230022,P.R.China 2.Postdoctoral Research Station of Management College,Hefei University of Technology,Anhui 230009,P.R.China Department of Mathematics Anhui University of Architecture Postdoctoral Research Station of Management College Hefei University of Technology

A gap theorem on complete noncompact n-dimensional locally conformally flat Riemannian manifold with nonnegative and bounded Ricci curvature is *** there holds the following condition：integral（sk（x0,s）ds= o（log ... 详细信息

关键词： Ricci curvature conformally flat gap theorem.

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共形平坦的黎曼流形

郑州大学学报（理学版） 1987年第2期28卷 20-22页

作者：李志波

设M是n>2维连通的微分流形。本文利用微分几何中的Bochner技巧证明了下述定理: 定理A.设M是n>2维紧致、共形平坦的黎曼流形,具常标量曲率,则M是常曲率黎曼流形。文献[1]证明了下述定理:设M是n≥3维紧致、共形平坦的黎曼流形,具有常标置... 详细信息

设M是n>2维连通的微分流形。本文利用微分几何中的Bochner技巧证明了下述定理: 定理A.设M是n>2维紧致、共形平坦的黎曼流形,具常标量曲率,则M是常曲率黎曼流形。文献[1]证明了下述定理:设M是n≥3维紧致、共形平坦的黎曼流形,具有常标置曲率r.如果RiCCi张量的长度小于r/2n-1,则M是常曲率的。 [1]文是用“夹击”（Pinch）Ricci张量的方法证明上述结果的。如定理A所示,在很自然的前提下（微分流形M是连通的）关于Ricci张量的长度的限制可以丢掉。

关键词： Constant scalar curvature conformally flat Space of scalar Curvature Quasi-negative function.