Bi-Legendrian manifolds and paracontact geometry

TL;DR

This paper explores the relationship between paracontact geometry and bi-Legendrian manifolds, revealing new insights and classes of examples by interpreting bi-Legendrian connections as paracontact connections.

Contribution

It establishes a correspondence between bi-Legendrian and paracontact structures, providing new examples and deepening understanding of their interplay.

Findings

Bi-Legendrian connection can be viewed as a paracontact connection.

New classes of paracontact manifolds are constructed.

Theoretical links between bi-Legendrian and paracontact geometries are clarified.

Abstract

We study the interplays between paracontact geometry and the theory of bi-Legendrian manifolds. We interpret the bi-Legendrian connection of a bi-Legendrian manifold M as the paracontact connection of a canonical paracontact structure induced on M and then we discuss many consequences of this result both for bi-Legendrian and for paracontact manifolds. Finally new classes of examples of paracontact manifolds are presented.