Abstract
We study a class of Finsler metrics which contains the class of P-reducible metrics. Finsler metrics in this class are called generalized P-reducible metrics. We consider generalized P-reducible metrics with scalar flag curvature and find a condition under which these metrics reduce to C-reducible metrics. This generalizes Matsumoto’s theorem, which describes the equivalency of C-reducibility and P-reducibility on Finsler manifolds with scalar curvature. Then we show that generalized P-reducible metrics with vanishing stretch curvature are C-reducible.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bejancu A., Farran H.: Generalized Landsberg manifolds of scalar curvature. Bull. Korean Math. Soc. 37, 543–550 (2000)
Berwald L.: Über Parallelübertragung in Räumen mit allgemeiner Massbestimmung. Jber. Deutsch. Math.-Verein. 34, 213–220 (1926)
Bidabad B., Tayebi A.: Properties of generalized Berwald connections. Bull. Iran. Math. Society 35, 237–254 (2009)
Matsumoto M.: On C-reducible Finsler spaces. Tensor, N.S. 24, 29–37 (1972)
Matsumoto M.: On Finsler spaces with Randers metric and special forms of important tensors. J. Math. Kyoto Univ. 14, 477–498 (1974)
Matsumoto M., Hōjō S.: A conclusive theorem for C-reducible Finsler spaces. Tensor. N.S. 32, 225–230 (1978)
Matsumoto M., Shimada H.: On Finsler spaces with the curvature tensors \({P_{hijk}}\) and \({S_{hijk}}\) satisfying special conditions. Rep. Math. Phys. 12, 77–87 (1977)
Matsumoto M.: An improvment proof of Numata and Shibata’s theorem on Finsler spaces of scalar curvature. Publ. Math. Debrecen 64, 489–500 (2004)
Mo X.: The flag curvature tensor on a closed Finsler space. Results in Math. 36, 149–159 (1999)
Najafi B., Shen Z., Tayebi A.: Finsler metrics of scalar flag curvature with special non-Riemannian curvature properties. Geom. Dedicata 131, 87–97 (2008)
Najafi B., Tayebi A.: Finsler Metrics of scalar flag curvature and projective invariants. Balkan Journal of Geometry and Its Applications 15, 90–99 (2010)
Prasad B.N.: Finsler spaces with the torsion tensor \({P_{ijk}}\) of a special form. Indian. J. Pur. Appl. Math. 11, 1572–1579 (1980)
Z. Shen, Differential Geometry of Spray and Finsler Spaces, Kluwer Academic (2001).
Tayebi A., Azizpour E., Esrafilian E.: On a family of connections in Finsler geometry. Publ. Math. Debrecen 72, 1–15 (2008)
Tayebi A., Najafi B.: Shen’s processes on Finslerian connection theory. Bull. Iran. Math. Soc. 36, 57–73 (2010)
Tayebi A., Peyghan E.: On Ricci tensors of Randers metrics. J. Geometry and Physics 60, 1665–1670 (2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Heydari, A., Peyghan, E. & Tayebi, A. Generalized P-reducible Finsler metrics. Acta Math. Hungar. 149, 286–296 (2016). https://doi.org/10.1007/s10474-016-0615-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10474-016-0615-0