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arXiv · 1510.06268

Lagrangian submanifolds in para-complex Euclidean space

Henri Anciaux·Maikel Samuays
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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 D^n and discuss a number of examples, such as graphs and normal bundles. We also characterize those Lagrangian surfaces of D^2 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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Henri Anciaux, Maikel Samuays. 2015-10-21. Lagrangian submanifolds in para-complex Euclidean space. https://arxiv.org/abs/1510.06268

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