Asian Journal of Mathematics

On the injectivicy radius growth of complete noncompact Riemannian manifolds

Abstract

In this paper we introduce a global geometric invariant $\alpha(M)$ related to injectivity radius to complete non-compact Riemannian manifolds and prove: If $\alpha(M^n) \gt 1$, then $M^n$ is isometric to $\mathbb{R}^n$ when Ricci curvature is non-negative, and is diffeomorphic to $\mathbb{R}^n$ for $n \neq 4$ and homeomorphic to $\mathbb{R}^4$ for $n = 4$ if without any curved assumption.

Article information

Source
Asian J. Math., Volume 18, Number 3 (2014), 419-426.

Dates
First available in Project Euclid: 8 September 2014