Biharmonic submanifolds in a Riemannian manifold
Differential Geometry
2014-08-26 v1
Abstract
In this paper, we solve affirmatively B.-Y. Chen's conjecture for hypersurfaces in the Euclidean space, under a generic condition. More precisely, every biharmonic hypersurface of the Euclidean space must be minimal if their principal curvatures are simple, and the associated frame field is irreducible.
Keywords
Cite
@article{arxiv.1408.5494,
title = {Biharmonic submanifolds in a Riemannian manifold},
author = {N. Koiso and H. Urakawa},
journal= {arXiv preprint arXiv:1408.5494},
year = {2014}
}
Comments
25 pages