Casorati curvatures of ideal submanifolds

Abstract

A. Mihai and I. Mihai (1999) have proved Chen inequalities for slant submanifolds in complex space forms M̃(c) of holomorphic sectional curvature c. Later, A. Mihai (2004) has investigated the case of slant submanifolds in generalized complex space forms. In the present paper, we study the conexion beetween the eigendirections of the extrinsic Casorati operator A^C and the eigendirections of the intrinsic Ricci tensor S of M, in the cases of ideal submanifolds in sense of Chen, who have specified above.