Lagrangian submanifolds in para-complex Euclidean space

2015/10/21 by Anciaux, Henri, Samuays, Maikel
#53A10 #53D12 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.06268

Abstract

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 the Lagrangian self-similar solutions of the Mean Curvature Flow which are SO(n)-equivariant.

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