Conformal Dirac Structures

Abstract

The Courant bracket defined originally on the sections of the vector bundle $TM\oplus T^{\ast }M\to M$ is extended to the direct sum of the 1-jet vector bundle and its dual. The extended bracket allows to interpret many structures encountered in differential geometry in terms of Dirac structures. We give here a new approach to conformal Jacobi structures.

23 pages, LateX

Cited by in corpus (11)

• Graded contact manifolds and contact Courant algebroids
• The graded Jacobi algebras and (co)homology
• Contact manifolds and generalized complex structures
• AV-Courant algebroids and generalized CR structures
• Integration of Dirac-Jacobi structures
• Differential graded contact geometry and Jacobi structures
• Lie algebroid foliations and ${\mathcal{E}}^1(M)$-Dirac structures
• Higher omni-Lie algebroids
• Gauge transformations of Jacobi structures and contact groupoids
• Jacobi Geometry and Hamiltonian Mechanics: the Unit-Free Approach
• The Deformation $L_{\infty }$ algebra of a Dirac--Jacobi structure