Illinois Journal of Mathematics

Open manifolds with asymptotically nonnegative curvature

Mahaman Bazanfaré

Full-text: Open access

Abstract

In this paper we establish a generalization of Toponogov's theorem for manifolds with asymptotically nonnegative sectional curvature, and we give a pinching condition under which asymptotically nonnegative curved manifolds are diffeomorphic to $\mathbb{R}^{n}$.

Article information

Source
Illinois J. Math., Volume 49, Number 3 (2005), 705-717.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138215

Digital Object Identifier
doi:10.1215/ijm/1258138215

Mathematical Reviews number (MathSciNet)
MR2210255

Zentralblatt MATH identifier
1155.53314

Subjects
Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]
Secondary: 31C12: Potential theory on Riemannian manifolds [See also 53C20; for Hodge theory, see 58A14] 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]

Citation

Bazanfaré, Mahaman. Open manifolds with asymptotically nonnegative curvature. Illinois J. Math. 49 (2005), no. 3, 705--717. doi:10.1215/ijm/1258138215. https://projecteuclid.org/euclid.ijm/1258138215


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