Geodesic mapping onto Kählerian spaces of the first kind

Zlatanović, Milan ; Hinterleitner, Irena ; Najdanović, Marija

Czechoslovak Mathematical Journal, Tome 64 (2014) no. 4, pp. 1113-1122

Abstract (VO)

In the present paper a generalized Kählerian 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 $\smash {F^h_i}$ that is covariantly constant with respect to the first kind of covariant derivative. \endgraf Using a non-symmetric metric tensor we find necessary and sufficient conditions for geodesic mappings $f\colon \mathbb {GR}_N\to \mathbb {G}\underset 1{\mathbb {\overline {K}}}_N$ 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 with respect to unknown components of the metric tensor and the complex structure of the Kählerian space $\mathbb {G}{\underset 1 {\mathbb {K}}}_N$.

Détail

DOI : 10.1007/s10587-014-0156-z

Classification : 53B05, 53B35
Keywords: geodesic mapping; equitorsion geodesic mapping; generalized Kählerian space

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