Conformal Change of the Finsler Space with an (α, β)-metric is of Douglas Type

Article Sidebar

PDF
Published: Jun 15, 2022
Keywords:
Finsler metric, Conformal change, Douglas space, Douglas space of second kind

Main Article Content

Ramdayal Singh Kushwaha
Department of Mathematics and Statistics, Banasthali Vidyapith, Jaipur, India
Renu
Department of Mathematics and Statistics, Banasthali Vidyapith, Jaipur, India

Abstract

Present work studies with the special (alpha, beta)-metric, defined by L=.......... Using the Chern and Shen’s lemma, we obtained the conditions for the special (alpha, beta)-metric to be the Finsler metric. Also, we have proved that a Douglas space of second kind with this metric is conformally transformed to a Douglas space of second kind.

Article Details

How to Cite
1.
Ramdayal Singh Kushwaha, Renu. Conformal Change of the Finsler Space with an (α, β)-metric is of Douglas Type. J. Int. Acad. Phys. Sci. [Internet]. 2022 Jun. 15 [cited 2024 May 19];26(2):135-44. Available from: https://www.iaps.org.in/journal/index.php/journaliaps/article/view/681
Issue
Vol. 26 No. 2 (2022): Table of Content
Section
Articles
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

References

S. Báscó and M. Matsumoto, On the Finsler spaces of Douglas type. A generalisation of the notion of the Berwald space, Publ. Math. Debrecen, 51 (1997) 358–406.

S. Báscó and M. Matsumoto, On Finsler spaces of Douglas type II. Projectively Flat Spaces, Publ. Math. Debrecen, 53 (1998) 423–438.

L. Berwald, On Cartan and Finsler geometries. III: Two-dimensional Finsler spaces with rectilinear extremal, Ann. of Math., 42 (1) (1941) 84–112.

M. Hashiguchi, On Conformal transformations of difference tensors of Finsler space, J. Math. Kyoto Univ., 16 (1976) 25–50.

M. S. Knebelman, Conformal geometry of generalized metric spaces, Proc. Nat. Acad. Sci. USA, 15 (1929) 376–379.

P. Kumar and B. K. Tripathi, Finsler spaces with some special (α,β)-metric of Douglas type, Malaya j. mat., 7 (2) (2019) 132–137.

Y. D. Lee, Conformal transformations of difference tensors of Finsler space with an (α,β)-metric, Comm. Korean Math. Soc., 21 (4) (1997) 975–984.

. I. Y. Lee, Douglas space of second kind of Finsler space with a Matsumoto metric, J. Chungcheong Math. soc., 21 (2) (2008) 209–221.

M. Matsumoto, The Berwald connection of a Finsler spaces with an (α,β)-metric, Tensor, N. S., 50 (1991) 18–21.

M. Matsumoto, Theory of Finsler spaces with (α,β)-metric, Rep. Math. Phys., 31 (1992) 43-83.

M. Matsumoto, Finsler spaces with an (α,β)-metric of Douglas type, Tensor, N. S., 60 (1998) 123–134.

B. N. Prasad, B. N. Gupta, and D. D. Singh, On conformal transformation in Finsler spaces with an (α,β)-metric, Indian J. Pure Appl. Math., 18 (4) (1987) 290–301.

G. Shanker and S. A. Baby, On the conformal change of Douglas space of second kind with special Finsler Space with special (α,β)-metric, AIP Conference Proceedings 2261, 030011, (2020) 1-8.

G. Shanker and D. Choudhary, On the conformal change of Douglas space of second kind with certain (α,β)-metrics, Int. J. Pure Appl. Math., 103 (4) (2015) 613–624.

G. Shanker and R. Yadav, On the Randers change of Exponential Metric, Appl. Sci., 15 (2013) 94–103.

G. Shanker and R. Yadav, Weakly Berwald Finsler spaces with first approximate Matsumoto metric, Tensor, N. S., 74 (1) (2013) 34–42.

K. R. Thippeswamy and S. K. Narasimhamurthy, Conformal change of Douglas special Finsler Space with Second Approximate Matsumoto metric, Int. J. Adv. Res., 5 (4) (2017) 1290–1295.