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Lagrangian submanifolds in para-complex Euclidean space

par Anciaux, Henri ;Samuays, Maikel Antonio
Référence Bulletin of the Belgian Mathematical Society Simon Stevin, 23, 3, page (421-437)
Publication Publié, 2016

Article révisé par les pairs

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Résumé :

We address the study of some curvature equations for distinguished submanifolds in para-Kähler geometry. We first observe that a para-complex submanifold of a para-Kähler manifold is minimal. Next we describe the extrinsic geometry of Lagrangian submanifolds in the para-complex Euclidean space Dn and discuss a number of examples, such as graphs and normal bundles. We also characterize those Lagrangian surfaces of D2 which are minimal and have indefinite metric. Finally we describe those Lagrangian self-similar solutions of the Mean Curvature Flow (with respect to the neutral metric of Dn) which are SO(n)-equivariant.