Lagrangian submanifolds in pseudo-Riemannian geometry

Abstract

The purpose of this project is the study of several variational problems related to Lagrangian submanifolds in certain pseudo-Riemannian manifolds, namely in pseudo-Kahler manifolds. Firstly, we plan to focus on the Hamiltonian stability of minimal or H-minimal Lagrangian submanifolds. In particular, we wish to prove the following conjecture: a H-minimal, non minimal Lagrangian submanifold is H-unstable, at least in some simple cases, e.g. when the ambient manifold is the pseudo-Euclidean complex space.In the second part of this project, we plan to study those Lagrangian submanifolds which solutions of some curvature equations as minimal, marginally trapped and H-minimal, aiming at finding several families of examples (e.g. those submanifolds which are invariant by the action of an isometry group) and hopefully give a characterization of these solutions. (AU)