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D-Recurrent Kropina Spaces with Generalized Douglas Metric

Year 2014, Volume: 1 Issue: 1, 17 - 21, 01.07.2016

Abstract

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.

References

  • [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
Year 2014, Volume: 1 Issue: 1, 17 - 21, 01.07.2016

Abstract

References

  • [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
There are 13 citations in total.

Details

Other ID JA49BD57AG
Journal Section Articles
Authors

Salim Ceyhan This is me

Gülçin Çivi This is me

Publication Date July 1, 2016
Submission Date July 1, 2016
Published in Issue Year 2014 Volume: 1 Issue: 1

Cite

APA Ceyhan, S., & Çivi, G. (2016). D-Recurrent Kropina Spaces with Generalized Douglas Metric. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, 1(1), 17-21.