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Symmetry in the geometry of metric contact pairs
Author(s) -
Bande Gianluca,
Blair David E.
Publication year - 2013
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201100300
Subject(s) - mathematics , pure mathematics , product (mathematics) , manifold (fluid mechanics) , metric (unit) , hermitian manifold , statistical manifold , symplectic geometry , closed manifold , symplectic manifold , mathematical analysis , topology (electrical circuits) , geometry , ricci curvature , invariant manifold , combinatorics , scalar curvature , information geometry , curvature , mechanical engineering , operations management , engineering , economics
We prove that the universal covering of a complete locally symmetric normal metric contact pair manifold with decomposable ϕ is a Calabi‐Eckmann manifold or the Riemannian product of a sphere and R . We show that a complete, simply connected, normal metric contact pair manifold with decomposable ϕ, 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 ϕ‐symmetric spaces or the product of a globally ϕ‐symmetric space and R . Moreover in the first case the manifold fibers over a locally symmetric space endowed with a symplectic pair.