Kodai Mathematical Journal

Bi-paracontact structures and Legendre foliations

Beniamino Cappelletti Montano

Full-text: Open access

Abstract

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.

Article information

Source
Kodai Math. J., Volume 33, Number 3 (2010), 473-512.

Dates
First available in Project Euclid: 5 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1288962554

Digital Object Identifier
doi:10.2996/kmj/1288962554

Mathematical Reviews number (MathSciNet)
MR2754333

Zentralblatt MATH identifier
1215.53074

Citation

Cappelletti Montano, Beniamino. Bi-paracontact structures and Legendre foliations. Kodai Math. J. 33 (2010), no. 3, 473--512. doi:10.2996/kmj/1288962554. https://projecteuclid.org/euclid.kmj/1288962554


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