A note on mean curvature, Maslov class and symplectic area of Lagrangian immersions

2003/10/03 by Kai Cieliebak, Cieliebak, Kai, Edward Goldstein +1 · 1 citation
Mathematics · #53XX #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DG #math.SG #msc:53XX

paper · pdf · doi:10.48550/arxiv.math/0310046

J. Symplectic Geom. vol 2 (2004), issue 2, 261-266

arxiv created 2004/12/03 · arxiv updated 2009/12/01

Abstract

In this note we prove a simple relation between the mean curvature form, symplectic area, and the Maslov class of a Lagrangian immersion in a Kähler-Einstein manifold. An immediate consequence is that in Kähler-Einstein manifolds with positive scalar curvature, minimal Lagrangian immersions are monotone.

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