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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References
Anderson, M;Cheeger, J.:C α-Compactness for Manifolds with Ricci Curvature and Injective Radius Bounded below.Geom. Funct. Anal. 1 (1991), 232–252.
Adams, R.:Sobolev Spaces. Academic Press, 1975.
Cheeger, J.;Gromoll, D.: The Splitting Theorem for Manifolds of Nonnegative Ricci Curvature.J. Differential Geom. 6 (1971), 119–128.
Fukaya, K.; Yamaguchi, T.:The Fundamental Groups of Almost Nonnegatively Curved Manifolds. Preprint, 1990.
Grove, K.; Petersen, V.:On the Excess of Metric Spaces and Manifolds. Preprint, 1989.
Gilbarg, D.;Trudinger, N.:Elliptic Partial Differential Equations of Second Order. 2nd Edition, Grundlehren Series, vol. 224, Springer-Verlag, New York 1986.
Treves, F.:Basic Linear Partial Differential Equations. Academic Press, New York 1975.
Shen, Z.;Wei, G.: On Riemannian Manifolds of Almost Nonnegative Curvature.Indiana Univ. Math. J. 40 (1991), 551–565.
Yamaguchi, T.: Collapsing and Pinching under a Lower Curvature Bound.Ann. of Math. 133 (1991), 317–357.
Yang, D.:Convergence of Riemannian Manifolds with Integral Bounds on Curvature. Preprint, 1989.
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Cai, M. A splitting theorem for manifolds of almost nonnegative Ricci curvature. Ann Glob Anal Geom 11, 373–385 (1993). https://doi.org/10.1007/BF00773552
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DOI: https://doi.org/10.1007/BF00773552