ON THE INFINITESIMAL ISOMETRIC DEFORMATIONS OF SUBMANIFOLDS

Acta mathematica scientia,Series B ›› 1997, Vol. 17 ›› Issue (4): 392-404.

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ON THE INFINITESIMAL ISOMETRIC DEFORMATIONS OF SUBMANIFOLDS

Chen Xinyue¹, Yang Wenmao²

1. Chongqing Institute of Industry and Management, Chongqing 650050, China;
2. Debt. of Math., Wuahn University, Wuhan 430072, China

Received:1995-11-22 Revised:1996-07-03 Online:1997-12-25 Published:1997-12-25

Abstract

Abstract: In this paper, we consider the infinitesimal Ⅰ-and Ⅱ-isometry deformations of submanifolds immersed in a space form N of constant curvature. We obtain some results which are new even in the case of N being the Euclidean space. At the same time, we generalize some classical results in E³ to the submanifolds immersed in a space form of constant curvature.

Key words: infinitesimal isometric deformation, mean curvature, Gauss-Kronecker curvature, sectional curvature

Chen Xinyue,Yang Wenmao. ON THE INFINITESIMAL ISOMETRIC DEFORMATIONS OF SUBMANIFOLDS[J].Acta mathematica scientia,Series B, 1997, 17(4): 392-404.

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ON THE INFINITESIMAL ISOMETRIC DEFORMATIONS OF SUBMANIFOLDS

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