On complex Kropina spaces

Abstract

In this paper we study the holomorphic curvature of the complex Kropina metrics. We find the conditions such that a complex Kropina space is weakly K¨ahler or moreover, Kahler. A special attention is devoted to a class of complex Kropina metrics with an additional assumption. We find a necessary and sufficient condition that such a complex Kropina metric should be weakly Kahler and also some outcomes about Kahler-Kropina metrics. At the end our results are applied to some examples, better illustrating the interest for this work.