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Homogeneous spaces of curvature bounded below

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Abstract

We prove that every locally connected quotient G/H of a locally compact, connected, first countable topological group G by a compact subgroup H admits a G-invariant inner metric with curvature bounded below. Every locally compact homogeneous space of curvature bounded below is isometric to such a space. These metric spaces generalize the notion of Riemannian homogeneous space to infinite dimensional groups and quotients which are never (even infinite dimensional) manifolds. We study the geometry of these spaces, in particular of non-negatively curved homogeneous spaces.

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Authors and Affiliations

  1. Omsk State University, Pr. Mira 55A, 644077, Omsk 77, Russia

    Valera Berestovskii

  2. Department of Mathematics, University of Tennessee, Ayres Hall 121, 37996-1306, Knoxville, TN, USA

    Conrad Plaut

Authors
  1. Valera Berestovskii
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  2. Conrad Plaut
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Correspondence to Valera Berestovskii.

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Dedicated to the memory of A. D. Alexandrov

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Berestovskii, V., Plaut, C. Homogeneous spaces of curvature bounded below. J Geom Anal 9, 203–219 (1999). https://doi.org/10.1007/BF02921936

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  • DOI: https://doi.org/10.1007/BF02921936

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