Subscribe

Subscribe to our Newsletter and get informed about new publication regulary and special discounts for subscribers!

IJPMS > Volume 18 > Projectively Flat Finsler Space of Douglas Type...
< Back to Volume

Projectively Flat Finsler Space of Douglas Type with Weakly-Berwald (α,β)-Metric

Full Text PDF

Abstract:

The present article is organized as follows: In the first part, we characterize the important class of special Finsler (α,β)-metric in the form of L=α+α2/β, where α is Riemannian metric and β is differential 1-form to be projectively flat. In the second part, we describe condition for a Finsler space Fn with an (α,β)-metric is of Douglas type. Further we investigate the necessary and sufficient condition for a Finsler space with an (α,β)-metric to be weakly-Berwald space and Berwald space.

Info:

Periodical:
International Journal of Pure Mathematical Sciences (Volume 18)
Pages:
1-12
Citation:
M. Ramesha and S.K. Narasimhamurthy, "Projectively Flat Finsler Space of Douglas Type with Weakly-Berwald (α,β)-Metric", International Journal of Pure Mathematical Sciences, Vol. 18, pp. 1-12, 2017
Online since:
Aug 2017
Export:
Distribution:
References:

[1] M. Hasiguchi, J. Ichijo, On some special (α, β)-metric, Rep. Fac. Sci. Kagasima Uni. Math. Phys. Chem. 8 (1975) 39-46.

[2] S. Kikuchi, On the condition that a space with (α, β)-metric be locally minkowskian, Tensors, N. S. 33(1) (1979) 242-246.

[3] C. Shibata, On Finsler space with an (α, β)-metric, J. Hokkaido Univ. of Education, IIA. 35 (1984) 1-16.

[4] P. Kumar et al., On a special hypersurface of a Finsler space with (α, β)-metric, Tbilisi Mathematical Journal. 2 (2009) 51-60.

[5] S.K. Narasimhamurthy, H.A. Kumar, On a hyper surface of special Finsler space with L = (α+β)2 α , International Journal of Mathematical Archive. 9 (2011) 1528-1535.

[6] H.S. Park, E.S. Choi, Finsler spaces with an approximate Matsumoto metric of Douglas type, Comm. Korean Math. Soc. 14 (3) (1999) 535-544.

[7] H.S. Park, I.Y. Lee, The Randers change of Finsler spaces with (α, β)-metrics of Douglas type, Journal of Korean Math. Soc. 38(3) (2001) 503-521.

[8] H.S. Park, E.S. Choi, Finsler spaces with the second approximate Matsumoto metric, Bull. Korean Math. Soc. 39(1) (2002) 153-163.

[9] I.Y. Lee, H.S. Park, Finsler spaces with Infinite series (α, β)-metric, J. Korean Math. Soc. 3 (2004) 567-589.

[10] H.G. Nagaraj, P. Kumar, On Randers change of Matsumoto metric, Bulletin of Mathematical Analysis and Applications. 4(1) (2012) 148-155.

[11] M. Matsumoto, Projective flat Finsler space with (α, β)-metric, Reports on mathematical physics. 30(1) (1991) 15-20.

[12] B.D. Kim, On the projectively flat Finsler space with a Special (α, β)-metric, Comm. Korean Math. Soc. 11(2) (1996) 407-413.

[13] H.S. Park, I.Y. Lee, On projectively flat Finsler space with a (α, β)-metric, Comm. Korean Math. Soc. 14 (2) (1999) 373-383.

[14] H.S. Park et al., Projectively flat Finsler space with a Certain (α, β)-metrics, Bull. Korean Math. Soc. 40(4) (2003) 649-661.

[15] S.K. Narasimhamurthy, G. N. Latha Kumari, C.S. Bagewadi, On Some Projectively flat (α, β)metrics, International Electronic Journal of Pure and Applied Mathematics. 3(3) (2011) 187-193.

[16] I.Y. Lee, M.H. Lee, On Weakly-Berwald spaces of special (α, β)-metric, Bull. Korean Math. Soc. 43 (2) (2006) 425-441.

[17] M. Matsumoto, The Berwald connection of a Finsler space with an (α, β)-metric, Tensors, N. S. 50(1) (1991) 18-21.

[18] S. Bacso, R. Yoshikawa, Weakly-Berwald spaces, Publicationes Mathematicae-Debrecen. 61(1- 2) (2002) 219-231.

[19] M. Matsumoto, Theory of Finsler space with (α, β)-metric, Reports on mathematical physics. 31 (1992) 43-83.

[20] S. Bacso, M. Matsumoto, On a Finsler spaces of Douglas type. A generalization of the notion of Berwald space, Publicationes Mathematicae-Debrecen. 51 (1997) 385-406.

[21] R. Yoshikawa, K. Okubo, M. Matsumoto, The conditions for some (α, β)-metric spaces to be Weakly-Berwald spaces, Tensor. New series. 65(3) (2004) 277-290.

[22] B. Tiwari, Manoj Kumar, On Finsler space with a special (α, β)-metric, Journal of the Indian Math. Soc. 82(3-4) (2015) 207-218.

[23] S.K. Narasimhamurthy, G. N. Latha Kumari, C. S. Bagewadi, Geometric properties of WeaklyBerwlad space with some (α, β)-metric, Tensor society. 05 (2011) 1-13.

[24] S. Bacso, M. Matsumoto, Projective changes between Finsler spaces with (α, β)-metric, Tensors, N.S. 55(3) (1994) 252-257.

[25] P.L. Antonelli, R.S. Ingarden, M. Matsumto, The theory of sprays and Finsler spaces with application in physics and biology, Kluwer acad. publ., Dordrecht, Boston, London, (1985).

Show More Hide