## 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