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

20 06 Bohr - Sommerfeld Star Products

We relate the Bohr-Sommerfeld conditions established in λ-microlocal analysis to formal deformation quantization of symplectic manifolds by classifying star products adapted to some Lagrangian sub-manifold L, i.e. products preserving the classical vanishing ideal IL of L up to IL-preserving equivalences.

Se p 19 99 Complexification of Bohr - Sommerfeld conditions .

The complex version of Bohr-Sommerfeld conditions is proposed. The BPU-construction (see [BPU] or [T1]) is generalized to this complexification. The new feature of this generalization is a spectral curve. The geometry of such curves is investigated. 1 Global structures on subspaces of Lagrangian cycles Let (M,ω) be a smooth symplectic manifold of dimesion 2n. It can be considered as a phase spa...

Bohr-sommerfeld Star Products

We relate the Bohr-Sommerfeld conditions established in λ-microlocal analysis to formal deformation quantization of symplectic manifolds by classifying star products adapted to some Lagrangian sub-manifold L, i.e. products preserving the classical vanishing ideal IL of L up to IL-preserving equivalences.

Maslov class of lagrangian embedding to Kahler manifold

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.