Tangent Dirac Structures and Poisson Dirac Submanifolds

Abstract

The local equations that characterize the submanifolds N of a Dirac manifold M is an isotropic (coisotropic) submanifold of TM endowed with the tangent Dirac structure. In the Poisson case which is a result of Xu: the submanifold N has a normal bundle which is a coisotropic submanifold of TM with the tangent Poisson structure if and only if N is a Dirac submanifold. In this paper we have proved a theorem in the general Poisson case that the fixed point set M^G has a natural induced Poisson structure that implies a Poisson-Dirac submanifolds, where G×M→M be a proper Poisson action.