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July 2014 On the injectivicy radius growth of complete noncompact Riemannian manifolds
Zhongyang Sun, Jianming Wan
Asian J. Math. 18(3): 419-426 (July 2014).

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.

Citation

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Zhongyang Sun. Jianming Wan. "On the injectivicy radius growth of complete noncompact Riemannian manifolds." Asian J. Math. 18 (3) 419 - 426, July 2014.

Information

Published: July 2014
First available in Project Euclid: 8 September 2014

zbMATH: 1370.53034
MathSciNet: MR3257833

Subjects:
Primary: 53C20
Secondary: 53C35

Rights: Copyright © 2014 International Press of Boston

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Vol.18 • No. 3 • July 2014
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