in this paper‎, ‎the‎ ‎authors prove that a strictly kähler-berwald manifold with‎ ‎nonzero constant holomorphic sectional curvature must be a‎ kähler manifold‎.

We obtain the expressions for sectional curvature, holomorphic sectional curvature, and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite Kaehler manifold. We discuss the boundedness of holomorphic sectional curvature of GCR-lightlike submanifolds of an indefinite complex space form. We establish a condition for a GCR-lightlike submanifold of an indefinite comple...

In this paper‎, ‎the‎ ‎authors prove that a strictly Kähler-Berwald manifold with‎ ‎nonzero constant holomorphic sectional curvature must be a‎ Kähler manifold‎. 

The study of holomorphic and isometric immersions of a Kähler manifold (M,g) into a Kähler manifold (N,G) started with Calabi. In his famous paper [3] he considered the case when the ambient space (N,G) is a complex space form, i.e. its holomorphic sectional curvature KN is constant. There are three types of complex space forms : flat, hyperbolic or elliptic according as the holomorphic section...

We characterize the natural diagonal almost product (locally product) structures on the tangent bundle of a Riemannian manifold. We obtain the conditions under which the tangent bundle endowed with the determined structure and with a metric of natural diagonal lift type is a Riemannian almost product (locally product) manifold, or an (almost) para-Hermitian manifold. We find the natural diagona...

We prove a Liouville property of holomorphic maps from a complete Kähler manifold with nonnegative holomorphic bisectional curvature to a complete simply connected Kähler manifold with a certain assumption on the sectional curvature.

In this paper we classify real hypersurfaces with constant totally real bisectional curvature in a non flat complex space formMm(c), c 6= 0 as those which have constant holomorphic sectional curvature given in [6] and [13] or constant totally real sectional curvature given in [11].