×

On homogeneous Finsler spaces. (English) Zbl 1137.53339

Summary: We study homogeneous Finsler spaces and show that they are forward complete. As a special case we consider homogeneous Randers spaces and show that if these spaces have constant flag curvature then the underlying Riemannian space is locally symmetric. Also we extend some of classical results in Riemannian homogeneous spaces to homogeneous Finsler spaces.

MSC:

53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
53C35 Differential geometry of symmetric spaces
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Antonelli, P. L.; Ingarden, R. S.; Matsumato, M., The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology, (FTPH, Vol. 58 (1993), Kluwer: Kluwer Dordecht) · Zbl 0821.53001
[2] Bao, D.; Chem, S. S.; Shen, Z., An Introduction to Riemann-Finsler Geometry, (GTM, Vol. 200 (2000), Springer: Springer Berlin) · Zbl 0954.53001
[3] Deng, S.; Hou, Z., The group of isometrics of a Finsler Space, Pac. J. Math., 207, 149 (2002) · Zbl 1055.53055
[4] Deng, S.; Hou, Z., Invariant Finsler metrics on homogeneous manifolds, J. Phys. A: Math. Gen., 37, 8245 (2004) · Zbl 1062.58007
[5] Deng, S.; Hou, Z., Invariant Randers metrics on homogeneous Riemannian manifolds, J. Phys. A: Math. Gen, 37, 4353 (2004) · Zbl 1049.83005
[6] Helgason, S., Differential Geometry, Lie Groups and Symmetric Spaces (1978), Academic Press: Academic Press New York · Zbl 0451.53038
[7] Kobayashi, S.; Nomizu, K., (Foundations of Differential Geometry, Vol. II (1969), Wiley: Wiley New York) · Zbl 0175.48504
[8] Latifi, D.; Razavi, A., A symmetric Finsler space with Chem connection, (Proceedings of the 3rd Seminar on Geometry and Topology (2004), Azerb. Univ. Tarbiat Moallem: Azerb. Univ. Tarbiat Moallem Tabriz), 231
[9] Loos, O., Symmetric Spaces I: General Theory (1969), Benjamin: Benjamin New York · Zbl 0175.48601
[10] Szabo, Z. I., Positive definite Berwald spaces, Tensor N.S., 35, 25 (1981) · Zbl 0464.53025
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.