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arXiv · 1512.02301

Biharmonic submanifolds of pseudo-Riemannian manifolds

Yuxin Dong·Ye-Lin Ou
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Abstract

In this paper, we derived biharmonic equations for pseudo-Riemannian submanifolds of pseudo-Riemannian manifolds which includes the biharmonic equations for submanifolds of Riemannian manifolds as a special case. As applications, we proved that a pseudo-umbilical biharmonic pseudo-Riemannian submanifold of a pseudo-Riemannian manifold has constant mean curvature, we completed the classifications of biharmonic pseudo-Riemannian hypersurfaces with at most two distinct principal curvatures, which were used to give four construction methods to produce proper biharmonic pseudo-Riemannian submanifolds from minimal submanifolds. We also made some comparison study between biharmonic hypersurfaces of Riemannian space forms and the space-like biharmonic hypersurfaces of pseudo-Riemannian space forms.

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Yuxin Dong, Ye-Lin Ou. 2015-12-08. Biharmonic submanifolds of pseudo-Riemannian manifolds. https://arxiv.org/abs/1512.02301

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