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

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

2003-10-03

arxiv.org/abs/math/0310046v3

Mathematics

Differential Geometry

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

Scientific paper

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
K\"ahler-Einstein manifold. An immediate consequence is that in
K\"ahler-Einstein manifolds with positive scalar curvature, minimal Lagrangian
immersions are monotone.

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