Geodesic graphs in Randers g.o. spaces

Zdeněk Dušek

Displaying similar documents to “Geodesic graphs in Randers g.o. spaces”

Uniform Finsler Hadamard manifolds

Daniel Egloff (1997)

Annales de l'I.H.P. Physique théorique

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On geodesic mappings of special Finsler spaces

Bácsó, Sándor

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The author previously studied with and [Publ. Math. 42, 139-144 (1993; Zbl 0796.53022)] the diffeomorphisms between two Finsler spaces $F^{n} = (M^{n}, L)$ and ${\bar{F}}^{n} = (M^{n}, \bar{L})$ which map the geodesics of $F^{n}$ to geodesics of ${\bar{F}}^{n}$ (geodesic mappings).Now, he investigates the geodesic mappings between a Finsler space $F^{n}$ and a Riemannian space ${\bar{ℝ}}^{n}$ . The main result of this paper is as follows: if $F^{n}$ is of constant curvature $K$ and the mapping $F^{n} \to {\bar{ℝ}}^{n}$ is a strongly geodesic mapping then $K = 0$ or $K \neq 0$ and $\bar{L} = e^{ϕ (x)} L$ .

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

Zdeněk Dušek, Oldřich Kowalski (2006)

Archivum Mathematicum

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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 $M = [SO (5) \times SO (2)] / U (2)$ and $M = [SO (4, 1) \times SO (2)] / U (2)$ . 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...

Structure of geodesics in weakly symmetric Finsler metrics on H-type groups

Zdeněk Dušek (2020)

Archivum Mathematicum

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Structure of geodesic graphs in special families of invariant weakly symmetric Finsler metrics on modified H-type groups is investigated. Geodesic graphs on modified H-type groups with the center of dimension $1$ or $2$ are constructed. The new patterns of algebraic complexity of geodesic graphs are observed.

Homogeneous Randers spaces admitting just two homogeneous geodesics

Zdeněk Dušek (2019)

Archivum Mathematicum

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The existence of a homogeneous geodesic in homogeneous Finsler manifolds was investigated and positively answered in previous papers. It is conjectured that this result can be improved, namely that any homogeneous Finsler manifold admits at least two homogenous geodesics. Examples of homogeneous Randers manifolds admitting just two homogeneous geodesics are presented.