Asian Journal of Mathematics

On the injectivicy radius growth of complete noncompact Riemannian manifolds

Zhongyang Sun and Jianming Wan

Full-text: Open access

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

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1410186664

Mathematical Reviews number (MathSciNet)
MR3257833

Zentralblatt MATH identifier
1370.53034

Subjects
Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]
Secondary: 53C35: Symmetric spaces [See also 32M15, 57T15]

Keywords
Injectivity radius complete non-compact manifold

Citation

Sun, Zhongyang; Wan, Jianming. On the injectivicy radius growth of complete noncompact Riemannian manifolds. Asian J. Math. 18 (2014), no. 3, 419--426. https://projecteuclid.org/euclid.ajm/1410186664


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