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 that result both for bi-Legendrian and for paracontact manifolds, as a classification of paracontact metric structures. Finally new classes of examples of paracontact manifolds are presented.
Bi-Legendrian structures and paracontact geometry
CAPPELLETTI MONTANO, BENIAMINO
2009
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 that result both for bi-Legendrian and for paracontact manifolds, as a classification of paracontact metric structures. Finally new classes of examples of paracontact manifolds are presented.
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