Maslov class and minimality in Calabi-Yau manifolds

Abstract

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.

16 pages To be published in Journal of Geometry and Physics

References in corpus (2)

• Mirror Symmetry is T-Duality
• Categorial mirror symmetry for K3 surfaces

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