A new characterization of the Berger sphere in complex projective space

We give a complete classification of Lagrangian immersions of homogeneous 3-manifolds (the Berger spheres, the Heisenberg group Nil3Nil3, the universal covering of the Lie group PSL(2,R)PSL(2,R) and the Lie group Sol3Sol3) in 3-dimensional complex space forms. As a corollary, we get a new characterization of the Berger sphere in complex projective space.