Symmetry in the geometry of metric contact pairs |
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Authors: | Gianluca Bande David E Blair |
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Institution: | 1. Università degli Studi di Cagliari, Dipartimento di Matematica e Informatica, , Via Ospedale 72, 09124 Cagliari, Italia;2. Department of Mathematics, Michigan State University, East Lansing, , MI 48824‐1027 USA |
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Abstract: | We prove that the universal covering of a complete locally symmetric normal metric contact pair manifold with decomposable ? is a Calabi‐Eckmann manifold or the Riemannian product of a sphere and . We show that a complete, simply connected, normal metric contact pair manifold with decomposable ?, such that the foliation induced by the vertical subbundle is regular and reflections in the integral submanifolds of the vertical subbundle are isometries, is the product of globally ?‐symmetric spaces or the product of a globally ?‐symmetric space and . Moreover in the first case the manifold fibers over a locally symmetric space endowed with a symplectic pair. |
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Keywords: | Metric contact pairs metric contact geometry locally symmetric spaces ϕ ‐symmetric spaces Vaisman manifolds 53C25 |
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