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

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

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

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.