Dirac Structure for Quasi-Jacobi Bialgebroid and Its Applications*

摘要

We introduce the notion of Dirac structure for a quasi-Jacobi bialgebroid, and through its characteristic pair, we give the necessary and sufficient conditions for a maximal isotropic subbundle to be a Dirac structure. Then we obtain reduced quasi Jacobi structures on the quotient manifold of the base manifold of a quasi-Jacobi bialgebroid by using these conditions. As ageneralization of proto bialgebroid and quasi-Jacobi bialgebroid, we give the definition of proto-Jacobi bialgebroid, and prove that the double of a proto-Jacobi bialgebroid is a Courant-Jacobi algebroid. Meanwhile we present some examples and applications.