Geodesic mapping onto Kählerian spaces of the first kind

Abstract

In the present paper a generalized Kählerian space GK 1 N of the first kind is considered as a generalized Riemannian space GR N with almost complex structure F h i that is covariantly constant with respect to the first kind of covariant derivative.Using a non-symmetric metric tensor we find necessary and sufficient conditions for geodesic mappings f : GR N → GK 1 N with respect to the four kinds of covariant derivatives. These conditions have the form of a closed system of partial differential equations in covariant derivatives with respect to unknown components of the metric tensor and the complex structure of the Kählerian space GK 1 N .