A conformal characterization of manifolds of constant sectional curvature

Xiaoyang Chen; Francisco Fontenele; Frederico Xavier

A conformal characterization of manifolds of constant sectional curvature

Differential Geometry 2020-05-05 v1

Authors: Xiaoyang Chen , Francisco Fontenele , Frederico Xavier

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.

Keywords

constant sectional curvature riemannian manifold conformal vector field isometry smooth functions

Cite

@article{arxiv.2005.01260,
  title  = {A conformal characterization of manifolds of constant sectional curvature},
  author = {Xiaoyang Chen and Francisco Fontenele and Frederico Xavier},
  journal= {arXiv preprint arXiv:2005.01260},
  year   = {2020}
}

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