D-Recurrent Kropina Spaces with Generalized Douglas Metric

Yıl 2014, Cilt: 1 Sayı: 1, 17 - 21, 01.07.2016

Salim Ceyhan Gülçin Çivi

Öz

In this paper, we obtain the necessary and sufficient condition for a D-recurrent Kropina space to be a generalized Douglas space. Further we prove equivalent conditions for a D-recurrent Kropina space with weak Berwald metric.

Anahtar Kelimeler

D-recurrent Finsler spaces, Douglas metrics, Generalized Douglas metrics, Kropina spaces, Weak

Kaynakça

• [1] S. Bácsó and M. Matsumoto, “On Finsler spaces of Douglas type. A generalization of the notion of Berwald space”, Publ. Math., Debrecen, vol. 53/3-4, pp.423-438 ,1998.
• [2] M. Matsumoto, “Finsler spaces with ( , )   metric of Douglas type”, Tensor, N.,S.,vol. 60,pp. 123-134 ,1998.
• [3] M. Matsumoto, “Theory of Finsler spaces with an ( , )   metric”, Rep. on Math.Phys., vol. 31, pp. 43-83, 1992.
• [4] M. Matsumoto, “The Berwald connection of a Finsler space with an ( , )   metric”, Tensor, N. S., vol.50, pp. 18-25 ,1991.
• [5] S. Ceyhan and G. Çivi, “On special Kropina Spaces”, Publ. Math., Debrecen, rewiev, 2014.
• [6] Z. Shen, Lectures on Finsler geometry, World Scientific, Singapore, New Jersey, London, Hong Kong, 2001.
• [7] Z. Shen, Differential geometry of spray and Finsler spaces, Kluwer Academic Publishers, Dordrecht, 2001.
• [8] Antonelli, P.L., Ingarden, R.S. and Matsumoto, M., The theory of sprays and Finsler spaces with applications in Physics and biology, Kluwer Acad. Publ. Dordrecht, 1993.
• [9] Najafi , B., Shen, Z. and Tayebi, A. ,“On a projective class of Finsler metrics”, Math. Subj. Class., preprint.
• [10] Kim, B-D. and Park, Ha-Y. “On special Finsler spaces with common geodesics”, Korean Math. Soc., vol.15, pp. 331-338,2000 .
• [11] Bácsó, S., and Matsumoto, M. ,“Projective changes between Finsler spaces with ( , )   metric”, Tensor, N.S., vol 55,1994.
• [12] Hashiguchi, M., Hojo, S. and Matsumoto, M., “Landsberg spaces of dimension two with ( , )   metric”, Tensor, N.S., vol. 57, pp.145-153,1996.
• [13] Yoshikawa, R., Okubo, K. and Matsumoto, M. “The conditions for some ( , )   spaces to be weakly-Berwald spaces”, Tensors, N., S., vol. 65, pp.278-290, 2004