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Noncompact manifolds with nonnegative Ricci curvature

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Abstract

Let (M, d) be a metric space. For 0 < r < R, let G(p, r, R) be the group obtained by considering all loops based at a point p ∈ M whose image is contained in the closed ball of radius r and identifying two loops if there is a homotopy between them that is contained in the open ball of radius R. In this article we study the asymptotic behavior of the G(p, r, R) groups of complete open manifolds of nonnegative Ricci curvature. We also find relationships between the G(p, r, R) groups and tangent cones at infinity of a metric space and show that any tangent cone at infinity of a complete open manifold of nonnegative Ricci curvature and small linear diameter growth is its own universal cover.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 93106, Santa Barbara, California

    William C. Wylie

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  1. William C. Wylie
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Communicated by Peter Petersen

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Wylie, W.C. Noncompact manifolds with nonnegative Ricci curvature. J Geom Anal 16, 535–550 (2006). https://doi.org/10.1007/BF02922066

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  • DOI: https://doi.org/10.1007/BF02922066

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