A Rigidity Theorem for Hypersurfaces in Higher Dimensional Space Forms

Pengfei Guan; Xi Sisi Shen

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arXiv · 1306.1581

A Rigidity Theorem for Hypersurfaces in Higher Dimensional Space Forms

Pengfei Guan·Xi Sisi Shen

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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 $n\ge 2$.

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Pengfei Guan, Xi Sisi Shen. 2013-06-07. A Rigidity Theorem for Hypersurfaces in Higher Dimensional Space Forms. https://arxiv.org/abs/1306.1581

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