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Maslov class and minimality in Calabi-Yau manifolds

Alessandro Arsie
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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.

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Alessandro Arsie. 2000-01-12. Maslov class and minimality in Calabi-Yau manifolds. https://doi.org/10.1016/s0393-0440(00)00003-6

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