English

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}
}

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25 pages