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On the injectivicy radius growth of complete noncompact Riemannian manifolds. (English) Zbl 1370.53034

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

MSC:

53C20 Global Riemannian geometry, including pinching
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