The Mean Curvature of the Second Fundamental Form of a hypersurface

2007/09/13 by Stefan Haesen, Haesen, Stefan, Steven Verpoort +1
Mathematics · Physics and Astronomy · #53A10 #53B25 #53C42 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0709.2107

openalex publication_date 2007/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Local Rigidity Theorems for Minimal Hypersurfaces

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