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Geodesic graphs in Randers g.o. spaces

Zdeněk Dušek (2020)

Commentationes Mathematicae Universitatis Carolinae

The concept of geodesic graph is generalized from Riemannian geometry to Finsler geometry, in particular to homogeneous Randers g.o. manifolds. On modified H-type groups which admit a Riemannian g.o. metric, invariant Randers g.o. metrics are determined and geodesic graphs in these Finsler g.o. manifolds are constructed. New structures of geodesic graphs are observed.

Geodesic graphs on special 7-dimensional g.o. manifolds

Zdeněk Dušek, Oldřich Kowalski (2006)

Archivum Mathematicum

In ( Dušek, Z., Kowalski, O. and Nikčević, S. Ž., New examples of Riemannian g.o. manifolds in dimension 7, Differential Geom. Appl. 21 (2004), 65–78.), the present authors and S. Nikčević constructed the 2-parameter family of invariant Riemannian metrics on the homogeneous manifolds M = [ SO ( 5 ) × SO ( 2 ) ] / U ( 2 ) and M = [ SO ( 4 , 1 ) × SO ( 2 ) ] / U ( 2 ) . They proved that, for the open dense subset of this family, the corresponding Riemannian manifolds are g.o. manifolds which are not naturally reductive. Now we are going to investigate the remaining metrics...

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 𝕂 1 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 𝔾 𝕂 ¯ 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...

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