arXiv subjects

Zdeněk Dušek

Publications and source records attributed to Zdeněk Dušek.

2 recordsLinked to original sources

arXiv2017

The affine approach to homogeneous geodesics in homogeneous Finsler spaces

In a recent paper, it was claimed that any homogeneous Finsler space of odd dimension admits a homogeneous geodesic through any point. For the proof, the algebraic method dealing with the reductive decomposition of the Lie algebra of the isometry group was used. However, the proof contains a serious gap. In the present paper, homogeneous geodesics in Finsler homogeneous spaces are studied using the affine method, which was developed in earlier papers by the author. The mentioned statement is proved correctly and it is further proved that any homogeneous Berwald space or homogeneous reversible Finsler space admits a homogeneous geodesic through any point.

math.DG↗

arXiv2012

The existence of light-like homogeneous geodesics in homogeneous Lorentzian manifolds

In previous papers, a fundamental affine method for studying homogeneous geodesics was developed. Using this method and elementary differential topology it was proved that any homogeneous affine manifold and in particular any homogeneous pseudo-Riemannian manifold admits a homogeneous geodesic through arbitrary point. In the present paper this affine method is refined and adapted to the pseudo-Riemannian case. Using this method and elementary topology it is proved that any homogeneous Lorentzian manifold of even dimension admits a light-like homogeneous geodesic. The method is illustrated in detail with an example of the Lie group of dimension 3 with an invariant metric, which does not admit any light-like homogeneous geodesic.

math.DG↗