The Journal of Geometric Analysis

, Volume 9, Issue 2, pp 203–219

Homogeneous spaces of curvature bounded below


DOI: 10.1007/BF02921936

Cite this article as:
Berestovskii, V. & Plaut, C. J Geom Anal (1999) 9: 203. doi:10.1007/BF02921936


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


Key Words and Phrases

locally compact grouphomogeneous spaceAlexandrov curvature bounded belowproductquotientnon-negative curvature

Copyright information

© Mathematica Josephina, Inc. 1999

Authors and Affiliations

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