A Rigidity Theorem for Hypersurfaces in Higher Dimensional Space Forms

Pengfei Guan; Xi Sisi Shen

A Rigidity Theorem for Hypersurfaces in Higher Dimensional Space Forms

Differential Geometry 2013-06-10 v1

Authors: Pengfei Guan , Xi Sisi Shen

Abstract

The classical Cohn-Vossen theorem states that two isometric compact convex surfaces in $\mathbb{R}^{3}$ are congruent. In this short note, we generalize the classical Cohn-Vossen Theorem to higher dimensional surfaces in space form $N^{n+1}(K)$ for $n\ge 2$ .

Keywords

convex geometry convex bodies hypersurfaces

Cite

@article{arxiv.1306.1581,
  title  = {A Rigidity Theorem for Hypersurfaces in Higher Dimensional Space Forms},
  author = {Pengfei Guan and Xi Sisi Shen},
  journal= {arXiv preprint arXiv:1306.1581},
  year   = {2013}
}

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5 pages

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