Biharmonic submanifolds with parallel mean curvature vector field in spheres

Details Biharmonic submanifolds with parallel mean curvature vector field in spheres Biharmonic submanifolds with parallel mean curvature vector field in spheres

2010-11-08

arxiv.org/abs/1011.1727v2

Mathematics

Differential Geometry

15 pages. Minor changes made and one section added

Scientific paper

We present some results on the boundedness of the mean curvature of proper biharmonic submanifolds in spheres. A partial classification result for proper biharmonic submanifolds with parallel mean curvature vector field in spheres is obtained. Then, we completely classify the proper biharmonic submanifolds in spheres with parallel mean curvature vector field and parallel Weingarten operator associated to the mean curvature vector field.

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