International Journal of Mathematics and Mathematical Sciences 
Volume 2005 (2005), Issue 22, Pages 3575-3586
doi:10.1155/IJMMS.2005.3575

Biharmonic submanifolds in 3-dimensional (κ,μ)-manifolds

K. Arslan,1 R. Ezentas,1 C. Murathan,1 and T. Sasahara2

 1Department of Mathematics, Faculty of Science, Uludag University, Bursa 16059, Turkey
2Department of Mathematics, Faculty of Science, Hokkaido University, Sappro 060-0810, Japan
Received 19 April 2005; Revised 11 October 2005

Abstract

Biharmonic maps between Riemannian manifolds are defined as critical points of the bienergy and generalized harmonic maps. In this paper, we give necessary and sufficient conditions for nonharmonic Legendre curves and anti-invariant surfaces of 3-dimensional (κ,μ)-manifolds to be biharmonic.