ON THE INJECTIVITY RADIUS GROWTH OF COMPLETE NONCOMPACT RIEMANNIAN MANIFOLDS

摘要

In this paper we introduce a global geometric invariant α(M) related to injectivity radius to complete non-compact Riemannian manifolds and prove: If α(M~n) > 1, then M~n is isometric to R~n when Ricci curvature is non-negative, and is diffeomorphic to R~n for n ≠ 4 and homeomorphic to R~4 for n = 4 if without any curved assumption.