The Journal of Geometric Analysis

, Volume 9, Issue 2, pp 203–219

Homogeneous spaces of curvature bounded below

Article

DOI: 10.1007/BF02921936

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

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

22D0553C2153C2353C70

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