LAGRANGIAN H-UMBILICAL SUBMANIFOLDS OF PARA-KAHLER MANIFOLDS

The notion of Lagrangian H-umbilical submanifolds of Kahler manifolds introduced in [3, 4] is closely related with several problems in Lagrangian geometry (cf. [7]). The classification of such submanifolds was done in a series of author's papers [3, 4, 5]. On the other hand, the study of Lagrangian submanifolds of para-Kahler manifolds was initiated very recently in [10]. In this paper we study Lagrangian H-submanifolds of para-Kahler manifolds. As results we prove several fundemental properties of such submanifolds. Moreover, we are able to classify Lagrangian H-umbilical submanifolds of the para-Kahler n-plane (E-n(2n), go, P) for n >= 3.