Maslov class and minimality in Calabi-Yau manifolds

Details Maslov class and minimality in Calabi-Yau manifolds Maslov class and minimality in Calabi-Yau manifolds

2000-01-12

arxiv.org/abs/math/0001069v1

Mathematics

Differential Geometry

16 pages To be published in Journal of Geometry and Physics

Scientific paper

10.1016/S0393-0440(00)00003-6

Generalizing the construction of the Maslov class for a Lagrangian embedding in a symplectic vector space, we prove that it is possible to give a consistent definition of this class for any Lagrangian submanifold of a Calabi-Yau manifold. Moreover, we prove that this class can be represented by the contraction of the Kaehler form associated to the Calabi-Yau metric, with the mean curvature vector field of the Lagrangian embedding. Finally, we suggest a possible generalization of the Maslov class for Lagrangian submanifolds of any symplectic manifold, via the mean curvature representation.

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