The Journal of Geometric Analysis

, Volume 9, Issue 2, pp 203–219 | Cite as

Homogeneous spaces of curvature bounded below

Article

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.

Math Subject Classifications

22D05 53C21 53C23 53C70 

Key Words and Phrases

locally compact group homogeneous space Alexandrov curvature bounded below product quotient non-negative curvature 

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Copyright information

© Mathematica Josephina, Inc. 1999

Authors and Affiliations

  1. 1.Omsk State UniversityOmsk 77Russia
  2. 2.Department of MathematicsUniversity of TennesseeKnoxvilleUSA

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