On locally conformal Kaehler space forms

Abstract

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.