Lagrangian submanifolds in pseudo-Riemannian geometry

• Grant number: 10/18752-0
• Support Opportunities: Regular Research Grants
• Duration: January 01, 2011 - December 31, 2012
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Henri Nicolas Guillaume Anciaux
• Grantee: Henri Nicolas Guillaume Anciaux
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

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)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

ANCIAUX, HENRI. SPACES OF GEODESICS OF PSEUDO- RIEMANNIAN SPACE FORMS AND NORMAL CONGRUENCES OF HYPERSURFACES. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 366, n. 5, p. 2699-2718, MAY 2014. (10/18752-0)

ANCIAUX, HENRI; GODOY, YAMILE. Marginally trapped submanifolds in Lorentzian space forms and in the Lorentzian product of a space form by the real line. Journal of Mathematical Physics, v. 56, n. 2, FEB 2015. (10/18752-0)

ANCIAUX, HENRI; GEORGIOU, NIKOS. Hamiltonian stability of Hamiltonian minimal Lagrangian submanifolds in pseudo- and para-Kahler manifolds. ADVANCES IN GEOMETRY, v. 14, n. 4, p. 587-612, OCT 2014. (10/18752-0, 10/08669-9)