The affine approach to homogeneous geodesics in homogeneous Finsler spaces

Zdeněk Dušek

Displaying similar documents to “The affine approach to homogeneous geodesics in homogeneous Finsler spaces”

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.

On geodesic mappings of recurrent Finsler spaces.

Bácsó, Sándor, Papp, Ildikó (1995)

Mathematica Pannonica

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Geodesic lines in D recurrent Finsler spaces.

Čomić, Irena (1989)

Publications de l'Institut Mathématique. Nouvelle Série

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Finsler spaces admitting a parallel vector field.

Kitayama, Masashi (1998)

Balkan Journal of Geometry and its Applications (BJGA)

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The $L$ -dual of an $(α, β)$ Finsler space of order two.

Masca, Ioana Monica, Sabau, Vasile Sorin, Shimada, Hideo (2007)

Balkan Journal of Geometry and its Applications (BJGA)

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Multiplicity and stability of closed geodesics on Finsler 2-spheres

Yiming Long (2006)

Journal of the European Mathematical Society

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A survey of recent progress on the multiplicity and stability problems for closed geodesics on Finsler 2-spheres is given.

Notes on new Finsler metric function.

Beil, R.G. (1997)

Balkan Journal of Geometry and its Applications (BJGA)

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Complete Finsler manifolds and adapted coordinates.

Bidabad, Behroz (2009)

Balkan Journal of Geometry and its Applications (BJGA)

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Different Kinds of the Covariant Differentations in Recurrent Finsler Spaces

Irena Čomić (1986)

Publications de l'Institut Mathématique

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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 $\bar{L} = e^{ϕ (x)} L$ .