Glasnik Matematicki, Vol. 37, No.2 (2002), 331-346.

ON A CHERN-TYPE PROBLEM FOR SPACE-LIKE KAEHLER SUBMANIFOLDS

Young Jin Suh

Abstract.   The purpose of this paper is to investigate a Chern type problem for space-like Kaehler submanifolds M in indefinite complex hyperbolic space CH_p^n+p(c), c > 0. Accordingly, we give better estimations of the squared norm of the second fundamental form of M in CH_p^n+p(c), c < 0.

2000 Mathematics Subject Classification.   53C50, 53C56.

Key words and phrases.   Semi-Kaehler manifold, totally real bisectional curvature, the squared norm, the second fundamental form, space-like submanifolds, totally geodesic.