Inequalities for the Casorati Curvature of Statistical Manifolds in Holomorphic Statistical Manifolds of Constant Holomorphic Curvature

In this paper, we prove some inequalities in terms of the normalized δ -Casorati curvatures (extrinsic invariants) and the scalar curvature (intrinsic invariant) of statistical submanifolds in holomorphic statistical manifolds with constant holomorphic sectional curvature. Moreover, we study the equality cases of such inequalities. An example on these submanifolds is presented.

KÄHLER SURFACES WITH QUASI CONSTANT HOLOMORPHIC CURVATURE

In the paper we describe Kahler QCH surfaces. We prove that any Calabi type and orthotoric Kahler surfaces are QCH Kahler surfaces. We also classify locally homogeneous QCH surfaces.

On locally conformal Kaehler space forms

The notion of a locally conformal Kaehler manifold (an l.c.K-manifold) in a Hermitian manifold has been introduced by I. Vaisman in 1976. In [2], K. Matsumoto introduced some results with the tensor Pij is hybrid. In this work, we give a generalisation about the results of an l.c.K-space form with the tensor Pij is not hybrid. Moreover, the Sato?s form of the holomorphic curvature tensor in almost Hermitian manifolds and l.c.K-manifolds are presented.