The Mean Curvature of the Second Fundamental Form of a hypersurface

Details The Mean Curvature of the Second Fundamental Form of a hypersurface The Mean Curvature of the Second Fundamental Form of a hypersurface

2007-09-13

arxiv.org/abs/0709.2107v3

Mathematics

Differential Geometry

25 pages; 2 figures. As compared to previous versions only minor corrections have been made. A shorter version of this article

Scientific paper

An expression for the first variation of the area functional of the second
fundamental form is given for a hypersurface in a semi-Riemannian space. The
concept of the "mean curvature of the second fundamental form" is then
introduced. Some characterisations of extrinsic hyperspheres in terms of this
curvature are given.

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