Topology of manifolds with asymptotically nonnegative Ricci curvature

zbMATH Open1334.53029arXiv0809.4558MaRDI QIDQ907863

Bazanfaré Mahaman

Publication date: 26 January 2016

Published in: African Diaspora Journal of Mathematics (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/0809.4558

zbMATH Keywords

critical pointasymptotically nonnegative curvaturedensity of rays

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (4)

A topological rigidity theorem on open manifolds with nonnegative Ricci curvature ⋮ Open manifolds with asymptotically nonnegative Ricci curvature and large volume growth ⋮ Topological properties of manifolds admitting a \(Y^x\)-Riemannian metric ⋮ Manifolds of positive Ricci curvature with quadratically asymptotically nonnegative curvature and infinite topological type

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