Tangent dirac structures and submanifolds

Research output: Contribution to journalArticlepeer-review


We write down the local equations that characterize the submanifolds N of a Dirac manifold M which have a normal bundle that is either a coisotropic or an isotropic submanifold of TM endowed with the tangent Dirac structure. In the Poisson case, these formulas once again prove 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 the presymplectic case it is the isotropy of the normal bundle which characterizes the corresponding notion of a Dirac submanifold. On the way, we give a simple definition of the tangent Dirac structure, make new remarks about it and establish its characteristic, local formulas for various interesting classes of submanifolds of a Dirac manifold.

Original languageEnglish
Pages (from-to)759-775
Number of pages17
JournalInternational Journal of Geometric Methods in Modern Physics
Issue number5
StatePublished - Oct 2005


  • Coisotropic submanifolds
  • Complete lift
  • Dirac structure
  • Isotropic submanifolds
  • Vertical lift

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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