## Abstract

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 language | English |
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Pages (from-to) | 759-775 |

Number of pages | 17 |

Journal | International Journal of Geometric Methods in Modern Physics |

Volume | 2 |

Issue number | 5 |

DOIs | |

State | Published - Oct 2005 |

## Keywords

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

## ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)