A Note On Obata's Rigidity Theorem I

Guoqiang Wu; Rugang Ye

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arXiv · 1203.5307

A Note On Obata's Rigidity Theorem I

Guoqiang Wu·Rugang Ye

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Abstract

In this note we present various extensions of Obata's rigidity theorem concerning the Hessian of a function on a Riemannian manifold. They include general rigidity theorems for the generalized Obata equation, and hyperbolic and Euclidean analogs of Obata's theorem. Besides analyzing the full rigidity case we also characterize the geometry and topology of the underlying manifold in more general situations.

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BibTeX RIS

Guoqiang Wu, Rugang Ye. 2012-04-07. A Note On Obata's Rigidity Theorem I. https://arxiv.org/abs/1203.5307

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