Unit Tangent Sphere Bundles and Two-Point Homogeneous Spaces |
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| Authors: | Boeckx E Perrone D Vanhecke L |
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| Institution: | 1. Department of Mathematics Celestijnenlaan, Katholieke Universiteit Leuven, 200B, 3001, Leuven, Belgium E-mail
2. Dipartimento di Matematica, Università degli Studi di Lecce, Via Provinciale Lecce-Arnesano, P.O. Box 193, 73100, Lecce, Italy E-mail
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| Abstract: | We characterize two-point homogeneous spaces, locally symmetric spaces, C and B-spaces via properties of the standard contact metric structure of their unit tangent sphere bundle. Further, under various conditions on a Riemannian manifold, we show that its unit tangent sphere bundle is a (locally) homogeneous contact metric space if and only if the manifold itself is (locally) isometric to a two-point homogeneous space. |
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