Classification results for biharmonic submanifolds in spheres

Details Classification results for biharmonic submanifolds in spheres Classification results for biharmonic submanifolds in spheres

2007-01-05

arxiv.org/abs/math/0701155v1

Mathematics

Differential Geometry

Dedicated to Professor Vasile Oproiu on his 65th birthday, 14 pages

Scientific paper

We classify biharmonic submanifolds with certain geometric properties in Euclidean spheres. For codimension 1, we determine the biharmonic hypersurfaces with at most two distinct principal curvatures and the conformally flat biharmonic hypersurfaces. We obtain some rigidity results for pseudo-umbilical biharmonic submanifolds of codimension 2 and for biharmonic surfaces with parallel mean curvature vector field. We also study the type, in the sense of B-Y. Chen, of compact proper biharmonic submanifolds with constant mean curvature in spheres.

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