a1 Department of Mathematics, Oita National College of Technology, 1666 Maki, Oita 870-0150, Japan e-mail: email@example.com
Biharmonic Lagrangian surfaces of constant mean curvature in complex space forms are classified. A further important point is that new examples of marginally trapped biharmonic Lagrangian surfaces in an indefinite complex Euclidean plane are obtained. This fact suggests that Chen and Ishikawa's classification of marginally trapped biharmonic surfaces  is not complete.
(Received December 12 2006)
(Revised May 09 2007)
(Accepted May 24 2007)