Biharmonic hypersurfaces with three distinct principal curvatures in Euclidean 5-space

A submanifold M-n of a Euclidean space E-m is said to be biharmonic if Delta(H) over right arrow = 0, where Delta is a rough Laplacian operator and (H) over right arrow denotes the mean curvature vector. In 1991, B.Y. Chen proposed a well-known conjecture that the only biharmonic submanifolds of Euclidean spaces are the minimal ones. In this paper, we prove that Chen's conjecture is true for the case of hypersurfaces with three distinct principal curvatures in Euclidean 5-spaces. (C) 2013 Elsevier B.V. All rights reserved.