zbMATH — the first resource for mathematics

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.

53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
53C35 Differential geometry of symmetric spaces
Full Text: DOI arXiv
[1] Antonelli, P.L.; Ingarden, R.S.; Matsumato, M., The theory of sprays and Finsler spaces with applications in physics and biology, () · Zbl 0821.53001
[2] Bao, D.; Chem, S.S.; Shen, Z., An introduction to Riemann-Finsler geometry, () · Zbl 0954.53001
[3] Deng, S.; Hou, Z., The group of isometrics of a Finsler space, Pac. J. math., 207, 149, (2002)
[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 New York · Zbl 0451.53038
[7] Kobayashi, S.; Nomizu, K., ()
[8] Latifi, D.; Razavi, A., A symmetric Finsler space with chem connection, (), 231
[9] Loos, O., Symmetric spaces I: general theory, (1969), 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.