Journal of the Mathematical Society of Japan

Lagrangian calculus on Dirac manifolds

Kyousuke UCHINO

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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

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

First available in Project Euclid: 14 September 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Dirac manifolds Poisson manifolds and Lagrangian submanifolds


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

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