Tangent Dirac Structures and Poisson Dirac Submanifolds

Authors

  • Md Showkat Ali Department of Mathematics, Dhaka University, Dhaka-1000
  • MG M Talukder Department of Mathematics, Comilla University, Comilla
  • MR Khan Department of Mathematics, Comilla University, Comilla

DOI:

https://doi.org/10.3329/dujs.v62i1.21955

Keywords:

Dirac structures, Poisson Dirac submanifolds, Poisson bracket

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 MG has a natural induced Poisson structure that implies a Poisson-Dirac submanifolds, where G×M?M be a proper Poisson action.

DOI: http://dx.doi.org/10.3329/dujs.v62i1.21955

Dhaka Univ. J. Sci. 62(1): 21-24, 2014 (January)

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Published

2015-02-07

How to Cite

Ali, M. S., Talukder, M. M., & Khan, M. (2015). Tangent Dirac Structures and Poisson Dirac Submanifolds. Dhaka University Journal of Science, 62(1), 21–24. https://doi.org/10.3329/dujs.v62i1.21955

Issue

Vol. 62 No. 1 (2014)

Section

Articles