Journal of the Mathematical Society of Japan

Lagrangian calculus on Dirac manifolds

Kyousuke UCHINO

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Abstract

We define notions of isotropic, coisotropic and lagrangian submanifolds of Dirac manifolds. Notion of Dirac manifolds, Dirac maps and Dirac relations are defined. Extending the isotropic calculus on presymplectic manifolds and the coisotropic calculus on Poisson manifolds to Dirac manifolds,we construct the lagrangian calculus on Dirac manifolds as an extension of the one on symplectic manifolds. We see that there are three natural categories of Dirac manifolds.

Article information

Source
J. Math. Soc. Japan, Volume 57, Number 3 (2005), 803-825.

Dates
First available in Project Euclid: 14 September 2006

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1158241936

Digital Object Identifier
doi:10.2969/jmsj/1158241936

Mathematical Reviews number (MathSciNet)
MR2139735

Zentralblatt MATH identifier
1081.53070

Subjects
Primary: 53D12: Lagrangian submanifolds; Maslov index
Secondary: 53D17: Poisson manifolds; Poisson groupoids and algebroids

Keywords
Dirac manifolds Poisson manifolds and Lagrangian submanifolds

Citation

UCHINO, Kyousuke. Lagrangian calculus on Dirac manifolds. J. Math. Soc. Japan 57 (2005), no. 3, 803--825. doi:10.2969/jmsj/1158241936. https://projecteuclid.org/euclid.jmsj/1158241936


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