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 CPn(4) as discovered by Oprea. We show that, for n >= 4, an n-dimensional Lagrangian submanifold in CPn (4) for which equality is attained at all points is necessarily minimal.