Homogeneous spaces of curvature bounded below |
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Authors: | Valera Berestovskii Conrad Plaut |
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Institution: | (1) Omsk State University, Pr. Mira 55A, 644077 Omsk 77, Russia;(2) Department of Mathematics, University of Tennessee, Ayres Hall 121, 37996-1306 Knoxville, TN, USA |
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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.
Dedicated to the memory of A. D. Alexandrov |
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Keywords: | Math Subject Classifications" target="_blank">Math Subject Classifications 22D05 53C21 53C23 53C70 |
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