Lagrangian H-umbilical submanifolds in complex space forms and pseudo-parallel cubic form

Lagrangian H-umbilical submanifolds in complex space forms, as the "simplest" Lagrangian submanifolds next to the geodesic ones, were introduced and determined by B.-Y. Chen. Many interesting examples belong to this class, such as the Whitney spheres, isotropic non-minimal immersions, and special Calabi product immersions. In this paper, such submanifolds are proved to be of a conformally flat, quasi-Einstein metric and the pseudo- parallel cubic form. As the main results, we find a geometric characterization of those submanifolds as not being of constant sectional curvature. Meanwhile, for Lagrangian submanifolds in complex space forms with pseudo-parallel cubic form, we completely determine the three dimensional case, and all dimensions for the conformally flat case. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.