Biharmonic submanifolds of pseudo-Riemannian manifolds

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• 作者：Yuxin Dong^a ; ^{yxdong@fudan.edu.cn} ; Ye-Lin Ou^b ; ^{yelin.ou@tamuc.edu}
• 关键词：58E20 ; 53C12
• 刊名：Journal of Geometry and Physics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：112
• 期：Complete
• 页码：252-262
• 全文大小：434 K
• 卷排序：112

文摘

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.