Maslov class of lagrangian embedding to Kahler manifold

Ju n 20 06 Universal Maslov class of Bohr - Sommerfeld lagrangian embedding to pseudo - Einstein manifold

Maslov class and minimality in Calabi - Yau manifolds

Generalizing the construction of the Maslov class [µ Λ ] for a La-grangian embedding in a symplectic vector space, we prove that it is possible to give a consistent definition of the class [µ Λ ] for any La-grangian submanifold of a Calabi-Yau manifold. Moreover, extending a result of Morvan in symplectic vector spaces, we prove that [µ Λ ] can be represented by i H ω, where H is the mean curva...

. SG ] 2 J ul 2 01 3 CONSTRUCTING EXACT LAGRANGIAN IMMERSIONS WITH FEW DOUBLE POINTS

We establish, as an application of the results from [13], an h-principle for exact Lagrangian immersions with transverse self-intersections and the minimal, or near-minimal number of double points. One corollary of our result is that any orientable closed 3-manifold admits an exact Lagrangian immersion into standard symplectic 6space R6st with exactly one transverse double point. Our constructi...

A Note on Mean Curvature, Maslov Class and Symplectic Area of Lagrangian Immersions

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 KählerEinstein manifolds with positive scalar curvature, minimal Lagrangian immersions are monotone.

Maslov Class Rigidity for Lagrangian Submanifolds via Hofer’s Geometry

In this work, we establish new rigidity results for the Maslov class of Lagrangian submanifolds in large classes of closed and convex symplectic manifolds. Our main result establishes upper bounds for the minimal Maslov number of displaceable Lagrangian submanifolds which are product manifolds whose factors each admit a metric of negative sectional curvature. Such Lagrangian submanifolds exist ...