Geodesic mapping onto K\"ahlerian space of the first kind

TL;DR

This paper explores geodesic mappings onto generalized K"ahlerian spaces of the first kind, establishing conditions using non-symmetric metrics and covariant derivatives within a complex geometric framework.

Contribution

It introduces necessary and sufficient conditions for geodesic mappings onto generalized K"ahlerian spaces of the first kind using non-symmetric metrics and covariant derivatives.

Findings

Derived conditions for geodesic mappings using non-symmetric metrics.

Extended the theory of K"ahlerian spaces to include generalized structures.

Analyzed covariant derivatives in the context of complex geometric mappings.

Abstract

In the present paper a generalized K\"ahlerian space $\mathbb{G}\underset 1 {\mathbb{K}}{}_N$ of the first kind is considered, as a generalized Riemannian space $\mathbb{GR}_N$ with almost complex structure $F^h_i$, that is covariantly constant with respect to the first kind of covariant derivative. Using the non-symmetric metric tensor we find necessary and sufficient conditions for a geodesic mapping $f:\mathbb{GR}_N\to \mathbb{G}\underset 1 {\mathbb{\bar{K}}}{}_N$ with respect to the four kinds of covariant derivatives.