  In this paper we first give a Bonnet theorem for conformal Lagrangian
surfaces in complex space forms, then we show that any compact Lagrangian
surface in the complex space form admits at most one other global isometric
Lagrangian surface with the same mean curvature form, unless the Maslov form is
conformal. These two Lagrangian surfaces are then called Lagrangian Bonnet
pairs. We also studied the question about Lagrangian Bonnet surfaces in
$\tilde{M}^2(4c)$, and obtain some interesting results.
