Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5500152 | Journal of Geometry and Physics | 2017 | 11 Pages |
Abstract
In this paper, we derived biharmonic equations for pseudo-Riemannian submanifolds of pseudo-Riemannian manifolds which include the biharmonic equations for submanifolds of Riemannian manifolds as special cases. 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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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Yuxin Dong, Ye-Lin Ou,