RIGIDITY OF COMPACT MINIMAL SUBMANIFOLDS IN A LOCALLY SYMMETRIC AND CONFORMALLY FLAT RIEMANN MANIFOLD

数学物理学报(英文版) ›› 1996, Vol. 16 ›› Issue (1): 89-96.

RIGIDITY OF COMPACT MINIMAL SUBMANIFOLDS IN A LOCALLY SYMMETRIC AND CONFORMALLY FLAT RIEMANN MANIFOLD

陈广华, 徐森林

Dept. of the Gifted Young, Dept of Math., Univ. of Sci. & Tech. of China, Hefei 230026, China

收稿日期:1993-07-20 修回日期:1994-03-16 出版日期:1996-03-25 发布日期:1996-03-25

RIGIDITY OF COMPACT MINIMAL SUBMANIFOLDS IN A LOCALLY SYMMETRIC AND CONFORMALLY FLAT RIEMANN MANIFOLD

Chen Guanghua, Xu Senlin

Dept. of the Gifted Young, Dept of Math., Univ. of Sci. & Tech. of China, Hefei 230026, China

Received:1993-07-20 Revised:1994-03-16 Online:1996-03-25 Published:1996-03-25

摘要/Abstract

摘要： The compact minimal submanifold in a locally symetric and conformally flat Riemann manifold is discussed in this paper.We get the Pinching constant for scalar curvature.The result of Li^[2] is generalized,but the method is completely different. Meanwhile,we get better conclusion than that of[3].We also research the Pinching problem for sectional curvature on compact minimal submanifolds in a unit sphere, partially improving the results of S.T.Yan^[4].

关键词: Locally symetric, conformally flat, minimal submanifold, scalar curvature, sectional curvature

Abstract: The compact minimal submanifold in a locally symetric and conformally flat Riemann manifold is discussed in this paper.We get the Pinching constant for scalar curvature.The result of Li^[2] is generalized,but the method is completely different. Meanwhile,we get better conclusion than that of[3].We also research the Pinching problem for sectional curvature on compact minimal submanifolds in a unit sphere, partially improving the results of S.T.Yan^[4].

Key words: Locally symetric, conformally flat, minimal submanifold, scalar curvature, sectional curvature

陈广华, 徐森林. RIGIDITY OF COMPACT MINIMAL SUBMANIFOLDS IN A LOCALLY SYMMETRIC AND CONFORMALLY FLAT RIEMANN MANIFOLD[J]. 数学物理学报(英文版), 1996, 16(1): 89-96.

Chen Guanghua, Xu Senlin. RIGIDITY OF COMPACT MINIMAL SUBMANIFOLDS IN A LOCALLY SYMMETRIC AND CONFORMALLY FLAT RIEMANN MANIFOLD[J]. Acta mathematica scientia,Series B, 1996, 16(1): 89-96.

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RIGIDITY OF COMPACT MINIMAL SUBMANIFOLDS IN A LOCALLY SYMMETRIC AND CONFORMALLY FLAT RIEMANN MANIFOLD

RIGIDITY OF COMPACT MINIMAL SUBMANIFOLDS IN A LOCALLY SYMMETRIC AND CONFORMALLY FLAT RIEMANN MANIFOLD

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