Classification results for biharmonic submanifolds in spheres
Differential Geometry
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/0701155,
title = {Classification results for biharmonic submanifolds in spheres},
author = {A. Balmuş and S. Montaldo and C. Oniciuc},
journal= {arXiv preprint arXiv:math/0701155},
year = {2007}
}
Comments
Dedicated to Professor Vasile Oproiu on his 65th birthday, 14 pages