13 research outputs found
On twisted contact groupoids and on integration of twisted Jacobi manifolds
We introduce the concept of twisted contact groupoids, as an extension either
of contact groupoids or of twisted symplectic ones, and we discuss the
integration of twisted Jacobi manifolds by twisted contact groupoids. We also
investigate the very close relationships which link homogeneous twisted Poisson
manifolds with twisted Jacobi manifolds and homogeneous twisted symplectic
groupoids with twisted contact ones. Some examples for each structure are
presented
Atiyah class of a Manin pair
A Courant algebroid with a Dirac structure is said to be a
Manin pair. We first discuss -Dorfman connections on predual vector bundles
and develop the corresponding Cartan calculus. This is then used in
relation to Courant-Dorfman cohomology to compute a cohomology class that
measures the obstruction to the existence of a compatible -Dorfman
connection on predual vector bundles extending a given -Dorfman action
on .Comment: Comments are welcom
Poisson brackets with prescribed Casimirs
We consider the problem of constructing Poisson brackets on smooth manifolds
with prescribed Casimir functions. If is of even dimension, we achieve
our construction by considering a suitable almost symplectic structure on ,
while, in the case where is of odd dimension, our objective is achieved by
using a convenient almost cosymplectic structure. Several examples and
applications are presented.Comment: 24 page
Reduction of Jacobi manifolds via Dirac structures theory
We first recall some basic definitions and facts about Jacobi manifolds,
generalized Lie bialgebroids, generalized Courant algebroids and Dirac
structures. We establish an one-one correspondence between reducible Dirac
structures of the generalized Lie bialgebroid of a Jacobi manifold
for which 1 is an admissible function and Jacobi quotient
manifolds of . We study Jacobi reductions from the point of view of Dirac
structures theory and we present some examples and applications.Comment: 18 page
On the geometric quantization of twisted Poisson manifolds
We study the geometric quantization process for twisted Poisson manifolds.
First, we introduce the notion of Lichnerowicz-twisted Poisson cohomology for
twisted Poisson manifolds and we use it in order to characterize their
prequantization bundles and to establish their prequantization condition. Next,
we introduce a polarization and we discuss the quantization problem. In each
step, several examples are presented
On a new relation between Jacobi and homogeneous Poisson manifolds
We establish a new, very close, relationship which links Jacobi structures and homogeneous Poisson structures defined on the same manifold and study the characteristic foliations of the related structures. Several examples of this construction are also given
Structure locale de variétés de Jacobi-Nijenhuis
After a brief review on the basic notions and the principal results concerning
the Jacobi manifolds, the relationship between homogeneous Poisson manifolds and
conformal Jacobi manifolds, and also the compatible Jacobi manifolds, we give a
generalization of some of these results needed for the contents of this paper. We
introduce the notion of Jacobi-Nijenhuis structure and we study the relation between
Jacobi-Nijenhuis manifolds and homogeneous Poisson-Nijenhuis manifolds.
We present a local classification of homogeneous Poisson-Nijenhuis manifolds and
we establish some local models of Jacobi-Nijenhuis manifolds