Biharmonic Submanifolds with Parallel Mean Curvature Vector in Pseudo-Euclidean Spaces

被引：0
作者：
Yu Fu
机构：
[1] Dongbei University of Finance and Economics,School of Mathematics and Quantitative Economics
来源：
Mathematical Physics, Analysis and Geometry | 2013年 / 16卷
关键词：
Biharmonic submanifolds; Parallel mean curvature vector; Marginally trapped surface; Pseudo-Euclidean space; 53D12; 53C40; 53C42;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we investigate biharmonic submanifolds in pseudo-Euclidean spaces with arbitrary index and dimension. We give a complete classification of biharmonic spacelike submanifolds with parallel mean curvature vector in pseudo-Euclidean spaces. We also determine all biharmonic Lorentzian surfaces with parallel mean curvature vector field in pseudo-Euclidean spaces.
引用
收藏
页码：331 / 344
页数：13
相关论文
共 49 条
  • [1] Arvanitoyeorgosa A(2007)Biharmonic Lorentzian hypersurfaces in Pac. J. Math. 229 2-220
  • [2] Defever F(2008)Classification results for biharmonic submanifolds in spheres, Israel J. Math. 168 201-61
  • [3] Kaimakamis G(2008)Classification results and new examples of proper biharmonic submanifolds in spheres Note Mat. 1 49-102
  • [4] Papantoniou V(2010)Properties of biharmonic submanifolds in spheres J. Geom. Symmetry Phys. 17 87-1705
  • [5] Balmus A(2010)Biharmonic hypersurfaces in 4-dimensional space forms Math. Nachr. 283 1696-876
  • [6] Montaldo S(2001)Biharmonic submanifolds of Int. J. Math. 12 867-123
  • [7] Oniciuc C(2002)Biharmonic submanifolds in spheres Israel J. Math. 130 109-188
  • [8] Balmuus A(1991)Some open problems and conjectures on submanifolds of finite type Soochow J. Math. 17 169-666
  • [9] Montaldo S(1973)On the surfaces with parallel mean curvature vector Indian Univ. Math. J. 22 655-875
  • [10] Oniciuc C(2008)Classification of marginally trapped Lorentzian flat surfaces in J. Math. Anal. Appl. 340 861-428
12345