Startseite Projective flatness of a new class of (α,β)-metrics
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Projective flatness of a new class of (α,β)-metrics

  • Laurian-Ioan Pişcoran und Vishnu Narayan Mishra ORCID logo EMAIL logo
Veröffentlicht/Copyright: 12. August 2017
Veröffentlichen auch Sie bei De Gruyter Brill

Abstract

In this paper we investigate a new (α,β)-metric F=β+aα2+β2α, where α=aijyiyj is a Riemannian metric; β=biyi is a 1-form and a(14,+) is a real scalar. Also, we investigate the relationship between the geodesic coefficients of the metric F and the corresponding geodesic coefficients of the metric α.

MSC 2010: 42C10; 46B07

Acknowledgements

The authors would like to thank the anonymous reviewers for their helpful and valuable comments and suggestions that greatly contributed to improving the final version of the paper. They would also like to thank the editors for their generous comments and support during the reviewing process.

References

[1] S. Bácsó and M. Matsumoto, On Finsler spaces of Douglas type—A generalization of the notion of Berwald space, Publ. Math. Debrecen 51 (1997), no. 3–4, 385–406. 10.5486/PMD.1997.1975Suche in Google Scholar

[2] I. Bucataru and R. Miron, Finsler-Lagrange Geometry. Applications to Dynamical Systems, Editura Academiei Române, Bucharest, 2007. Suche in Google Scholar

[3] Deepmala and L. N. Mishra, Differential operators over modules and rings as a path to the generalized differential geometry, Facta Univ. Ser. Math. Inform. 30 (2015), no. 5, 753–764. Suche in Google Scholar

[4] M. Hashiguchi and Y. Ichijyō, Randers spaces with rectilinear geodesics, Rep. Fac. Sci. Kagoshima Univ. (1980), no. 13, 33–40. Suche in Google Scholar

[5] V. K. Kropina, On projective Finsler spaces with a metric of some special form (in Russian), Nauchn. Dokl. Vyssh. Shk. Fiz. Mat. Nauki 2 (1959), 38–42. Suche in Google Scholar

[6] B. Li, Projectively flat Matsumoto metric and its approximation, Acta Math. Sci. Ser. B Engl. Ed. 27 (2007), no. 4, 781–789. 10.1016/S0252-9602(07)60075-7Suche in Google Scholar

[7] M. Matsumoto, Projective changes of Finsler metrics and projectively flat Finsler spaces, Tensor (N.S.) 34 (1980), no. 3, 303–315. Suche in Google Scholar

[8] M. Matsumoto, Foundations of Finsler Geometry and Special Finsler Spaces, Kaiseisha Press, Shigaken, 1986. Suche in Google Scholar

[9] M. Matsumoto, A slope of a mountain is a Finsler surface with respect to a time measure, J. Math. Kyoto Univ. 29 (1989), no. 1, 17–25. 10.1215/kjm/1250520303Suche in Google Scholar

[10] M. Matsumoto, Finsler spaces with (α,β)-metric of Douglas type, Tensor (N.S.) 60 (1998), no. 2, 123–134. Suche in Google Scholar

[11] P. Senarath, Differential geometry of projectively related Finsler spaces, Ph.D. Thesis, Massey University, 2003, http://mro.massey.ac.nz/bitstream/handle/10179/1918/02_whole.pdf?sequence=1. Suche in Google Scholar

[12] Z. Shen, On projectively flat (α,β)-metrics, Canad. Math. Bull. 52 (2009), no. 1, 132–144. 10.4153/CMB-2009-016-2Suche in Google Scholar

[13] W. Song and X. Wang, A new class of Finsler metrics with scalar flag curvature, J. Math. Res. Appl. 32 (2012), no. 4, 485–492. Suche in Google Scholar

[14] A. Tayebi and H. Sadeghi, On generalized Douglas–Weyl (α,β)-metrics, Acta Math. Sin. (Engl. Ser.) 31 (2015), no. 10, 1611–1620. 10.1007/s10114-015-3418-2Suche in Google Scholar

Received: 2015-07-14
Revised: 2015-12-07
Accepted: 2015-12-10
Published Online: 2017-08-12
Published in Print: 2019-03-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 30.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/gmj-2017-0034/html
Button zum nach oben scrollen