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CONTACT METRIC (κ,μ)-SPACES AS BI-LEGENDRIAN MANIFOLDS

Part of: Global differential geometry

Published online by Cambridge University Press:  01 June 2008

BENIAMINO CAPPELLETTI MONTANO  and
LUIGIA DI TERLIZZI
BENIAMINO CAPPELLETTI MONTANO*
Affiliation:
Department of Mathematics, University of Bari, Via E. Orabona, 4, I-70125 Bari, Italy (email: [email protected])
LUIGIA DI TERLIZZI
Affiliation:
Department of Mathematics, University of Bari, Via E. Orabona, 4, I-70125 Bari, Italy (email: [email protected])
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Abstract

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We describe a contact metric manifold whose Reeb vector field belongs to the (κ,μ)-nullity distribution as a bi-Legendrian manifold and we study its canonical bi-Legendrian structure. Then we characterize contact metric (κ,μ)-spaces in terms of a canonical connection which can be naturally defined on them.

Keywords

contact metric (κ,μ)-manifolds(κ,μ)-nullity distributionLegendrian foliationsbi-Legendrian structures

MSC classification

Secondary: 53C12: Foliations (differential geometric aspects) 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 77 , Issue 3 , June 2008 , pp. 373 - 386
Copyright
Copyright © 2008 Australian Mathematical Society

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