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Geodesic mapping onto Kählerian spaces of the first kind

Milan Zlatanović; Irena Hinterleitner; Marija Najdanović — 2014

Czechoslovak Mathematical Journal

In the present paper a generalized Kählerian space $𝔾 {\underset{1}{𝕂}}_{N}$ of the first kind is considered as a generalized Riemannian space ${𝔾ℝ}_{N}$ with almost complex structure $F_{i}^{h}$ 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 $f : {𝔾ℝ}_{N} \to 𝔾 {\underset{1}{\bar{𝕂}}}_{N}$ 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...

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