Diffeomorphic theorems for open Riemannian manifolds with curvature decay

• Autores: C. Wu, Z. Xie, G. Li
• Localización: Publicationes Mathematicae Debrecen, ISSN 0033-3883, Tomus 79, Fasc. 1-2, 2011, págs. 133-144
• Idioma: inglés
• DOI: 10.5486/pmd.2011.4971
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• Resumen

  • In this paper, we study the topology of complete non-compact Riemannian manifolds with curvature decay to a non-positive constant. We show that such a complete open manifold M is diffeomorphic to a Euclidean n-space Rn if it contains enough rays starting from the base point. As applications, we also show that this kind of manifolds with Ricci curvature bounded from below by a non-positive constant are diffeomorphic to Rn if the volumes of geodesic balls in M grow properly. Our results generalize the main theorems of Wang�Xia for manifolds with quadratic curvature decay to zero.