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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

minimal submanifolds in Locally Symmetric Spaces

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Northeastern Mathematical Journal 2005年第1期21卷 61-69页

作者：纪永强徐森林 Department of Mathematics Huzhou Teacher's College Zhejiang 313000 Department of Mathematics University of Science and Technology of China Hefei 230026

In this paper, we discuss the compact minimal submanifolds in locally symmetric Riemannian manifolds. Two Pinching theorems are obtained and two corresponding results of Chern, S. S. and Yau S. T. are generalized.

关键词： locally symmetrical minimal submanifold totally geodesic

C_∞ Compactness for minimal submanifolds in the Unit Sphere

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Journal of Mathematical Research and Exposition 2003年第2期23卷 191-198页

作者：徐森林梅加强华中师范大学数学系湖北武汉430079 南京大学数学系江苏南京210093

In this paper we study the C3 compactness for minimal submanifolds in the unit sphere. We obtain two compactness theorems. As an application, we prove that there is a positive number δ(n), such that if the square of the length of the second fundamental form of a minimal subrnanifold in the unit sphere is less than 2n/3+δ(n), it must be totally geodesic or diffeomorphic to a Veronese surface.

关键词： minimal submanifold totally geodesic compactness theorem.

Equivariant Lagrangian minimal S^3 in CP^3

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Acta Mathematica Sinica,English Series 2006年第4期22卷 1215-1220页

作者： Zhen Qi LI Yong Qian TAO Department of Mathematics Nanchang University Nanchang 330047 P. R. China

The equivariant Lagrangian minimal immersion of Sa into *** is studied. The complete classification and analytic expression for such kinds of immersions are given.

关键词： complex projective space equivariant lagrangian minimal submanifold

Spectral Characterizations of Veronese Surface in S^4

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Journal of Shanghai University(English Edition) 2001年第1期5卷 29-30页

作者： ZHENGYong－ai LIUYu－rong 等 DepartmentofMathematics CollegeofScienceShanghaiUniversityShanghai200436China DepartmentofMathematics YangzhouUniversityYangzhou225003China

In this paper, we prove that the Veronese surface can be determined by the 1 spectrum of the Laplace operator.

关键词： minimal submanifold spectral characterization Veronese surface second fundamental form

A Pinching Theorem for minimal submanifolds in Sphere

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Communications in Mathematical Research 1998年第4期 112-117页

作者：许志才

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＭｂｅａｎｎ－ｄｉｍｅｎｓｉｏｎａｌｃｌｏｓｅｄｍｉｎｉｍａｌｙｉｍｍｅｒｓｅｄｓｕｂｍａｎｉｆｏｌｄｉｎｔｈｅｕｎｉｔｓｐｈｅｒｅＳｎ＋ｐ，Ｓｔｈｅｓｅｑｕｒｅｏｆｔｈｅｌｅｎｇ... 详细信息

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＭｂｅａｎｎ－ｄｉｍｅｎｓｉｏｎａｌｃｌｏｓｅｄｍｉｎｉｍａｌｙｉｍｍｅｒｓｅｄｓｕｂｍａｎｉｆｏｌｄｉｎｔｈｅｕｎｉｔｓｐｈｅｒｅＳｎ＋ｐ，Ｓｔｈｅｓｅｑｕｒｅｏｆｔｈｅｌｅｎｇｔｈｏｆｔｈｅｓｅｃｏｎｄｆｕｎｄ...

关键词： minimal submanifold Gauss Mapping Ricci Curvature Totally Geodesic submanifold

Two theorems on cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of Cayley algebra

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Journal of Harbin Institute of Technology(New Series) 2001年第1期8卷 38-40页

作者： Mihail Banaru (Smolensk University of Humanities, Smolensk 214014, Russia) Smolensk University of Humanities

Proves that cosymplectic hypersurfaces of six dimensional Hermitian submanifolds of the octave algebra are ruled manifolds and establishes a necessary and sufficient condition for a cosymplectic hypersurface of Hermit... 详细信息

关键词： Hermitian manifold almost contact metric structure ruled manifold minimal submanifold cosymplectic structure

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