Displaying similar documents to “Homogeneous Randers spaces admitting just two homogeneous geodesics”

The affine approach to homogeneous geodesics in homogeneous Finsler spaces

Zdeněk Dušek (2018)

Archivum Mathematicum

Similarity:

In the recent paper [Yan, Z.: Existence of homogeneous geodesics on homogeneous Finsler spaces of odd dimension, Monatsh. Math. 182,1, 165–171 (2017)], it was claimed that any homogeneous Finsler space of odd dimension admits a homogeneous geodesic through any point. However, the proof contains a serious gap. The situation is a bit delicate, because the statement is correct. In the present paper, the incorrect part in this proof is indicated. Further, it is shown that homogeneous geodesics...

Geodesic graphs in Randers g.o. spaces

Zdeněk Dušek (2020)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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.

Homogeneous variational problems and Lagrangian sections

D.J. Saunders (2016)

Communications in Mathematics

Similarity:

We define a canonical line bundle over the slit tangent bundle of a manifold, and define a Lagrangian section to be a homogeneous section of this line bundle. When a regularity condition is satisfied the Lagrangian section gives rise to local Finsler functions. For each such section we demonstrate how to construct a canonically parametrized family of geodesics, such that the geodesics of the local Finsler functions are reparametrizations.