The third fundamental form metric for hypersurfaces in nonflat space forms

被引：0

作者：

Liu H.L. ^{[1
]}

Simon U. ^{[3
]}

Verstraelen L. ^{[2
]}

Wang G.P. ^{[4
]}

机构：

[1] Department of Mathematics, Northeast University

[2] Dep. Wiskunde KU Leuven, B-3001 Leuven

[3] TU Berlin, MA 8-3, D-10623 Berlin

[4] Department of Mathematics, Beijing University

来源：

Journal of Geometry | 1999年 / 65卷 / 1-2期

关键词：

Codazzi tensor; Einstein metric; Hypersurfaces in nonflat space forms; Isoparametric hypersurfaces; Third fundamental form metric;

D O I：

10.1007/BF01228684

中图分类号：

学科分类号：

摘要：

For hypersurfaces with regular Weingarten operator in nonflat space forms we study the relations between the intrinsic geometry of the third fundamental form metric and the extrinsic geometry of the hypersurface. We prove a theorema-egregium-type result for this metric and, in particular, give a local classification of hypersurfaces in case of an Einstein structure of this metric. 1991 Mathematics Subject Classification. 53 B 25, 53 C 42, 53 C 25. © Birkhäuser Verlag, 1999.

引用

页码：130 / 142

页数：12

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