TOPOLOGY OF MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE RICCI CURVATURE

Bazanfare Mahaman (1, 2)

1 UAM - Abdou Moumouni University of Niamey = Université Abdou Moumouni de Niamey
2 IRMAR - Institut de Recherche Mathématique de Rennes

In this paper, we study the topology of complete noncompact Riemannian manifolds with asymptotically nonnegative Ricci curvature. We show that a complete noncompact manifold with asymptoticaly nonnegative Ricci curvature and sectional curvature decay at most quadratically is diffeomorphic to a Euclidean n-space R^n under some conditions on the density of rays starting from the base point p or on the volume growth of geodesic balls in M.

Mots clés: Asymptotically nonnegative Ricci Curvature; Critical point; Excess function

Domaines: Géométrie différentielle [math.DG]

Bazanfare Mahaman. TOPOLOGY OF MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE RICCI CURVATURE. African Diaspora Journal of Mathematics, 2015, 18 (2), pp.11-17. ⟨hal-00324963⟩