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arXiv · 2005.01260

A conformal characterization of manifolds of constant sectional curvature

Xiaoyang Chen·Francisco Fontenele·Frederico Xavier
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Abstract

A special case of the main result states that a complete $1$-connected Riemannian manifold $(M^n,g)$ is isometric to one of the models $\mathbb R^n$, $S^n(c)$, $\mathbb H^n(-c)$ of constant curvature if and only if every $p\in M^n$ is a non-degenerate maximum of a germ of smooth functions whose Riemannian gradient is a conformal vector field.

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Xiaoyang Chen, Francisco Fontenele, Frederico Xavier. 2020-05-04. A conformal characterization of manifolds of constant sectional curvature. https://arxiv.org/abs/2005.01260

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