African Diaspora Journal of Mathematics

Topology of Manifolds with Asymptotically Nonnegative Ricci Curvature

Bazanfaré Mahaman and Mamadou Mboup

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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

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

First available in Project Euclid: 7 December 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Asymptotically nonnegative curvature density of rays critical point


Mahaman, Bazanfaré; Mboup, Mamadou. Topology of Manifolds with Asymptotically Nonnegative Ricci Curvature. Afr. Diaspora J. Math. (N.S.) 18 (2015), no. 2, 11--17.

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