Korean J. Math. Vol. 32 No. 4 (2024) pp.661-671
DOI: https://doi.org/10.11568/kjm.2024.32.4.661

Berwald and Douglas spaces of a Finsler space with an exponential form of $(\alpha,\beta)$- metric

Article Sidebar

PDF
Published: Dec 30, 2024
Keywords:
Finsler space, Berwald space, Douglas space, ($\alpha$,$\beta$)-metric, Exponential ($\alpha$,$\beta$)-metric
Mathematics Subject Classification:
53B40, 53C60

Main Article Content

Brijesh Kumar Tripathi
Department of Mathematics, L.D. College of Engineering, Ahmedabad (Gujarat)-380015, India.
Dhruvisha Patel
Science Mathematics Branch, Gujarat Technological University, Ahmedabad, (Gujarat)-382424, India.

Abstract

In the present paper, we have undertaken a study of Berwald space and Douglas space in a Finsler space with exponential form of ($\alpha$, $\beta$)-metric. We have examined the conditions under which this metric will be a Berwald and Douglas space.



Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.

References

[1] P. L. Antonelli, R. S. Iugarden, M. Matsumoto, The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology, Kluwer Academic Publishers, Dordrecht, 1993. https://dx.doi.org/10.1007/978-94-015-8194-3 Google Scholar

[2] S. Bácsó, M. Matsumoto, Projective changes between Finsler space with (α,β)-metric, Tensor, N. S. 55 (1994), 252–257. Google Scholar

[3] S. Bácsó, M. Matsumoto, On the Finsler spaces of Douglas type. A generalization of the notion of Berwald space, Publ. Math. Debrecen 51 (1997), 385–406. Google Scholar

[4] L. Berwald, Parallelübertragung in allgemeinen Räumen, Atti Congr. Intern. Mat. Bologna 4 (1928), 263–270. Google Scholar

[5] P. Kumar, B. K. Tripathi, Finsler spaces with some special (α, β) metric of Douglas type, Malaya J. Math. 7 (2019), 132–137. https://dx.doi.org/10.26637/mjm0702/0001 Google Scholar

[6] I. Y. Lee, H. S. Park, Finsler spaces with infinite series (α, β)-metric, J. Korean Math. Soc. 41 (3) (2004), 567–589. https://dx.doi.org/10.4134/jkms.2004.41.3.567 Google Scholar

[7] I. Y. Lee, M. H. Lee, On Weakly-Berwald spaces of special (α,β)-metric, Bull. Korean Math. Soc. 43 (2) (2006), 425–441. https://dx.doi.org/10.4134/bkms.2006.43.2.425 Google Scholar

[8] M. Matsumoto, Theory of Finsler spaces with (α, β)-metric, Rep. Math. Phys. 31 (1992), 43–83. https://dx.doi.org/10.1016/0034-4877(92)90005-l Google Scholar

[9] M. Matsumoto, A slope of Mountain is a Finsler surface with respect to time measure, J. Math. Kyoto Univ. 29 (1) (1989), 17–25. https://dx.doi.org/10.1215/kjm/1250520303 Google Scholar

[10] M. Matsumoto, Foundations of Finsler Geometry and Special Finsler spaces, Kaiseisha Press, Otsu, Japan, 1986. Google Scholar

[11] M. Matsumoto, The Berwald connection of a Finsler space with an (α, β)-metric, Tensor, N. S. 50 (1991), 18–21. Google Scholar

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

[13] H. S. Park, E. S. Choi, Finsler spaces with an approximate Matsumoto metric of Douglas type, Comm. Korean Math. Soc. 14 (1999), 535–544. https://ckms.kms.or.kr/journal/view.html?uid=867 Google Scholar

[14] Z. Shen, G. Civi Yildirim, On a Class of Projectively Flat metrics with Constant Flag Curvature, Can. J. Math. 60 (2008), 443–456. https://dx.doi.org/10.4153/cjm-2008-021-1 Google Scholar

[15] B. K. Tripathi, Hypersurfaces of a Finsler Space with exponential form of (α,β)-Metric, Ann. Univ. Craiova Math. Comput. Sci. Ser. 47 (1) (2020), 132–140. Google Scholar

[16] B. K. Tripathi, S. Khan, On Weakly Berwald Space with a Special Cubic (α,β)-Metric, Surv. Math. Appl. 18 (2023), 1–11. https://www.utgjiu.ro/math/sma/v18/p18_01.pdf Google Scholar

[17] B. K. Tripathi, P. Kumar, Douglas Spaces For Some (α,β)-Metric of a Finsler Space, J. Adv. Math. Stud. 15 (4) (2022), 444–455. https://www.journal.fairpartners.ro/volume-152022-no-4_37.html Google Scholar