Characterizing warped-product Lagrangian immersions in complex projective space

Starting from two Lagrangian immersions and a horizontal curve in S 3 (1), it is possible to construct a new Lagrangian immersion, which we call a warped-product Lagrangian immersion. In this paper, we find two characterizations of warped-product Lagrangian immersions. We also investigate Lagrangian submanifolds which attain at every point equality in the improved version of Chen's inequality for Lagrangian submanifolds of ℂ P n (4) as discovered by Opreaffi We show that, for n ≥4, an n -dimensional Lagrangian submanifold in ℂ P n (4) for which equality is attained at all points is necessarily minimal.