A Note On Obata's Rigidity Theorem I
Differential Geometry
2012-04-10 v2
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.
Cite
@article{arxiv.1203.5307,
title = {A Note On Obata's Rigidity Theorem I},
author = {Guoqiang Wu and Rugang Ye},
journal= {arXiv preprint arXiv:1203.5307},
year = {2012}
}
Comments
Some remarks are added. A few typos are removed. The proof of one lemma is modified