Homogeneous spaces of curvature bounded below
- Cite this article as:
- Berestovskii, V. & Plaut, C. J Geom Anal (1999) 9: 203. doi:10.1007/BF02921936
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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.