On a Generalized ?R- Birecurrent Finsler Space
Keywords:
Finsler space, Generalized βR-birecurrent Finsler space, Ricci tensor, Landsberg space, Finsler space of scalar curvature.Abstract
In the present paper, we introduced a Finsler space whose Cartan's third curvature tensor satisfies
.
where and are non-zero covariant tensor fields of second order called recurrence tensor fields, such space is called as a generalized birecurrent Finsler space.
The curvature tensor , the torsion tensor ,the deviation tensor , the Ricci tensors ( , the vector and the scalar curvature tensor of such space are non-vanishing. Under certain conditions, a generalized birecurrent Finsler space becomes Landsberg space . Some conditions have been pointed out which reduce a generalized birecurrent Finsler space into Finsler space of scalar curvature.
References
[1]. A.G. Walker. On Ruse's space of recurrent curvature, Proc. Land Math. Soc., 52 ,1950,pp. 36-64.
[2]. B.B.Sinha and S.P.Singh '' On recurrent spaces of second order in Finsler space.'' Yakohama Math. J.,vol. 18,pp. 27-32, 1970.
[3]. F.Y.A .Qasem and A.A.M.Saleem'' On U- birecurrent Finsler space.'' Univ. Aden J. Nat. and Appl . Sc.Vol.14 No.3 ,December. 2010.
[4]. H.S .Ruse. Three dimensional spaces of recurrent curvature: Proc. Lond. Math. Soc., 50, 1949,pp. 438-446.
[5]. P. N. Pandey. A recurrent Finsler manifold admitting special recurrent transformation: Prog . Math.,13 (1-2) , 1979 ,pp. 85-98.
[6]. P. N. Pandey . A note on recurrence vector : proc. Nat. Acad. Sci. 51A,I , 1981,pp. 6-8.
[7]. P. N. Pandey.'' Some problems in Finsler spaces.'' D.Sc. Thesis, University of Allahabad, India ,1993.
[8]. P.N. Pandey, S. Saxena, and A. Goswani ''On a Generalized H-Recurrent space.'' Journal of International Academy of physical Science, Vol. 15, pp. 201-211, 2011.
[9]. R .B. Misra. On a recurrent Finsler spaces :Rev .Roumhaine Math. Pures Appl.18 ,1973,pp.701 -712.
[10]. R.S.D. Dubey and A.K. Srivastava. On recurrent Finsler spaces: Bull. Soc.Math. Belgique ,1981,pp. 283-288.
[11]. R.S. Mishra and H.D. Pande ''Recurrent Finsler space.'' J, India Math. Soc. N.S. vol.32, pp.17-22, 1968.
[12]. R. Verma ''Some transformations in Finsler spaces.'' Ph.D. Thesis, University of Allahabad, ,India, 1991.
[13]. S. Dikshit ''Certain types of recurrences in Finsler spaces.'' Ph.D. Thesis, University of Allahabad, 1992 .
[14]. Y .C. Worg . Linear connections with zero torsion and recurrent curvature : Trans . Amer . Math. Soc ., 102 ,1962, pp.471 – 506.
[15]. Y .C .Worg and K. Yano. projectively flat spaces with recurrent curvature : Comment Math . Helv .,35 ,1961, pp. 223 – 232 .
[2]. B.B.Sinha and S.P.Singh '' On recurrent spaces of second order in Finsler space.'' Yakohama Math. J.,vol. 18,pp. 27-32, 1970.
[3]. F.Y.A .Qasem and A.A.M.Saleem'' On U- birecurrent Finsler space.'' Univ. Aden J. Nat. and Appl . Sc.Vol.14 No.3 ,December. 2010.
[4]. H.S .Ruse. Three dimensional spaces of recurrent curvature: Proc. Lond. Math. Soc., 50, 1949,pp. 438-446.
[5]. P. N. Pandey. A recurrent Finsler manifold admitting special recurrent transformation: Prog . Math.,13 (1-2) , 1979 ,pp. 85-98.
[6]. P. N. Pandey . A note on recurrence vector : proc. Nat. Acad. Sci. 51A,I , 1981,pp. 6-8.
[7]. P. N. Pandey.'' Some problems in Finsler spaces.'' D.Sc. Thesis, University of Allahabad, India ,1993.
[8]. P.N. Pandey, S. Saxena, and A. Goswani ''On a Generalized H-Recurrent space.'' Journal of International Academy of physical Science, Vol. 15, pp. 201-211, 2011.
[9]. R .B. Misra. On a recurrent Finsler spaces :Rev .Roumhaine Math. Pures Appl.18 ,1973,pp.701 -712.
[10]. R.S.D. Dubey and A.K. Srivastava. On recurrent Finsler spaces: Bull. Soc.Math. Belgique ,1981,pp. 283-288.
[11]. R.S. Mishra and H.D. Pande ''Recurrent Finsler space.'' J, India Math. Soc. N.S. vol.32, pp.17-22, 1968.
[12]. R. Verma ''Some transformations in Finsler spaces.'' Ph.D. Thesis, University of Allahabad, ,India, 1991.
[13]. S. Dikshit ''Certain types of recurrences in Finsler spaces.'' Ph.D. Thesis, University of Allahabad, 1992 .
[14]. Y .C. Worg . Linear connections with zero torsion and recurrent curvature : Trans . Amer . Math. Soc ., 102 ,1962, pp.471 – 506.
[15]. Y .C .Worg and K. Yano. projectively flat spaces with recurrent curvature : Comment Math . Helv .,35 ,1961, pp. 223 – 232 .
Downloads
Published
2016-05-04
How to Cite
Qasem, F. Y. A., & Hadi, W. H. A. (2016). On a Generalized ?R- Birecurrent Finsler Space. American Scientific Research Journal for Engineering, Technology, and Sciences, 19(1), 9–18. Retrieved from https://asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/1433
Issue
Section
Articles
License
Authors who submit papers with this journal agree to the following terms.
