On the generalized Chen's conjecture on biharmonic submanifolds
Differential Geometry
2014-05-05 v3
Abstract
The generalized Chen's conjecture on biharmonic submanifolds asserts that any biharmonic submanifold of a non-positively curved manifold is minimal (see e.g., [CMO1], [MO], [BMO1], [BMO2], [BMO3], [Ba1], [Ba2], [Ou1], [Ou2], [IIU]). In this paper, we prove that this conjecture is false by constructing foliations of proper biharmonic hyperplanes in a 5-dimensional conformally flat space with negative sectional curvature. Many examples of proper biharmonic submanifolds of non-positively curved spaces are also given.
Keywords
Cite
@article{arxiv.1006.1838,
title = {On the generalized Chen's conjecture on biharmonic submanifolds},
author = {Ye-Lin Ou and Liang Tang},
journal= {arXiv preprint arXiv:1006.1838},
year = {2014}
}
Comments
revised version with a new title of the paper and journal reference. Michigan Math Journal, 2012