Geometric structures associated to a contact metric (κ,μ)-space

Beniamino Cappelletti Montano and Luigia Di Terlizzi

Vol. 246 (2010), No. 2, 257–292

DOI: 10.2140/pjm.2010.246.257

Abstract

We prove that any contact metric (κ,μ)-space (M,φ,ξ,η,g) admits a canonical paracontact metric structure that is compatible with the contact form η. We study this canonical paracontact structure, proving that it satisfies a nullity condition and induces on the underlying contact manifold (M,η) a sequence of compatible contact and paracontact metric structures satisfying nullity conditions. We then study the behavior of that sequence, which is related to the Boeckx invariant I_M and to the bi-Legendrian structure of (M,φ,ξ,η,g). Finally we are able to define a canonical Sasakian structure on any contact metric (κ,μ)-space whose Boeckx invariant satisfies |I_M| > 1.

Keywords

contact metric manifold, (κ,μ)-nullity condition, Sasakian, paracontact, para-Sasakian, bi-Legendrian, foliation, antihypercomplex, 3-web

Mathematical Subject Classification 2000

Primary: 53C12, 53C15, 53C25, 53C26

Secondary: 57R30

Milestones

Received: 4 April 2009

Accepted: 2 March 2010

Published: 1 June 2010