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arxiv: math/0310046 · v3 · submitted 2003-10-03 · 🧮 math.DG · math.SG

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

classification 🧮 math.DG math.SG
keywords curvaturelagrangianahler-einsteinareaclassimmersionsmaslovmean
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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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