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 › peer-review

6 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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title = "A splitting theorem for manifolds of almost nonnegative Ricci curvature",

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.",

keywords = "MSC 1991: 53C20, Manifolds of almost nonnegative Ricci curvature, splitting",

author = "Mingliang Cai",

year = "1993",

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doi = "10.1007/BF00773552",

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T1 - A splitting theorem for manifolds of almost nonnegative Ricci curvature

AU - Cai, Mingliang

PY - 1993/11/1

Y1 - 1993/11/1

N2 - 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.

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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DO - 10.1007/BF00773552

M3 - Article

AN - SCOPUS:0005612096

VL - 11

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EP - 385

JO - Annals of Global Analysis and Geometry

JF - Annals of Global Analysis and Geometry

SN - 0232-704X

IS - 4

ER -

A splitting theorem for manifolds of almost nonnegative Ricci curvature

Abstract

Keywords

ASJC Scopus subject areas

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