Open Access
October 2010 Bi-paracontact structures and Legendre foliations
Beniamino Cappelletti Montano
Kodai Math. J. 33(3): 473-512 (October 2010). DOI: 10.2996/kmj/1288962554


We study almost bi-paracontact structures on contact manifolds. We prove that if an almost bi-paracontact structure is defined on a contact manifold (M, η), then under some natural assumptions of integrability M carries two transverse bi-Legendrian structures. Conversely, if two transverse bi-Legendrian structures are defined on a contact manifold, then M admits an almost bi-paracontact structure. We define a canonical connection on an almost bi-paracontact manifold and we study its curvature properties, which resemble those of the Obata connection of a para-hypercomplex (or complex-product) manifold. Further, we prove that any contact metric manifold whose Reeb vector field belongs to the (κ, μ)-nullity distribution canonically carries an almost bi-paracontact structure and we apply the previous results to the theory of contact metric (κ, μ)-spaces.


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Beniamino Cappelletti Montano. "Bi-paracontact structures and Legendre foliations." Kodai Math. J. 33 (3) 473 - 512, October 2010.


Published: October 2010
First available in Project Euclid: 5 November 2010

zbMATH: 1215.53074
MathSciNet: MR2754333
Digital Object Identifier: 10.2996/kmj/1288962554

Rights: Copyright © 2010 Tokyo Institute of Technology, Department of Mathematics

Vol.33 • No. 3 • October 2010
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