African Diaspora Journal of Mathematics

Topology of Manifolds with Asymptotically Nonnegative Ricci Curvature

Bazanfaré Mahaman and Mamadou Mboup

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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 $M$ with asymptotically nonnegative Ricci curvature and sectional curvature $K(x)\ge \frac{C}{d_{p}(x)^{\alpha}}$ is diffeomorphic to the Euclidean space $\mathbb{R}^n$ under some conditions on the density of rays starting from the base point $p$ or on the volume growth of geodesic balls in $M$.

Article information

Source
Afr. Diaspora J. Math. (N.S.), Volume 18, Number 2 (2015), 11-17.

Dates
First available in Project Euclid: 7 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.adjm/1449496747

Mathematical Reviews number (MathSciNet)
MR3423733

Zentralblatt MATH identifier
1334.53029

Subjects
Primary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60] 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]

Keywords
Asymptotically nonnegative curvature density of rays critical point

Citation

Mahaman, Bazanfaré; Mboup, Mamadou. Topology of Manifolds with Asymptotically Nonnegative Ricci Curvature. Afr. Diaspora J. Math. (N.S.) 18 (2015), no. 2, 11--17. https://projecteuclid.org/euclid.adjm/1449496747


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