A splitting theorem for manifolds of almost nonnegative Ricci curvature

Mingliang Cai

doi:10.1007/BF00773552

A splitting theorem for manifolds of almost nonnegative Ricci curvature

Mingliang Cai

Mathematics

Research output: Contribution to journal › Article

5 Scopus citations

Abstract

Cheeger and Gromoll proved that a closed Riemannian manifold of nonnegative Ricci curvature is, up to a finite cover, diffeomorphic to a direct product of a simply connected manifold and a torus. In this paper, we extend this theorem to manifolds of almost nonnegative Ricci curvature.

Original language	English (US)
Pages (from-to)	373-385
Number of pages	13
Journal	Annals of Global Analysis and Geometry
Volume	11
Issue number	4
DOIs	https://doi.org/10.1007/BF00773552
State	Published - Nov 1 1993

Keywords

MSC 1991: 53C20
Manifolds of almost nonnegative Ricci curvature
splitting

ASJC Scopus subject areas

Analysis
Political Science and International Relations
Geometry and Topology

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10.1007/BF00773552

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Cai, M. (1993). A splitting theorem for manifolds of almost nonnegative Ricci curvature. Annals of Global Analysis and Geometry, 11(4), 373-385. https://doi.org/10.1007/BF00773552

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abstract = "Cheeger and Gromoll proved that a closed Riemannian manifold of nonnegative Ricci curvature is, up to a finite cover, diffeomorphic to a direct product of a simply connected manifold and a torus. In this paper, we extend this theorem to manifolds of almost nonnegative Ricci curvature.",

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AU - Cai, Mingliang

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AB - Cheeger and Gromoll proved that a closed Riemannian manifold of nonnegative Ricci curvature is, up to a finite cover, diffeomorphic to a direct product of a simply connected manifold and a torus. In this paper, we extend this theorem to manifolds of almost nonnegative Ricci curvature.

KW - MSC 1991: 53C20

KW - Manifolds of almost nonnegative Ricci curvature

KW - splitting

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