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Article

The Existence of Two Homogeneous Geodesics in Finsler Geometry

Institute of Technology and Business in České Budějovice, Okružní 517/10, 370 01 České Budějovice, Czech Republic
Symmetry 2019, 11(7), 850; https://doi.org/10.3390/sym11070850
Received: 31 May 2019 / Revised: 21 June 2019 / Accepted: 24 June 2019 / Published: 1 July 2019
(This article belongs to the Special Issue Geometry of Submanifolds and Homogeneous Spaces)
The existence of a homogeneous geodesic in homogeneous Finsler manifolds was positively answered in previous papers. However, the result is not optimal. In the present paper, this result is refined and the existence of at least two homogeneous geodesics in any homogeneous Finsler manifold is proved. In a previous paper, examples of Randers metrics which admit just two homogeneous geodesics were constructed, which shows that the present result is the best possible. View Full-Text
Keywords: homogeneous manifold; homogeneous Finsler space; homogeneous geodesic homogeneous manifold; homogeneous Finsler space; homogeneous geodesic
MDPI and ACS Style

Dušek, Z. The Existence of Two Homogeneous Geodesics in Finsler Geometry. Symmetry 2019, 11, 850. https://doi.org/10.3390/sym11070850

AMA Style

Dušek Z. The Existence of Two Homogeneous Geodesics in Finsler Geometry. Symmetry. 2019; 11(7):850. https://doi.org/10.3390/sym11070850

Chicago/Turabian Style

Dušek, Zdeněk. 2019. "The Existence of Two Homogeneous Geodesics in Finsler Geometry" Symmetry 11, no. 7: 850. https://doi.org/10.3390/sym11070850

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