Special projective algebra of exponential metrics of isotropic S-curvature

Document Type : Original Article

Authors

Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

Abstract

Exponential metrics are popular Finsler metrics. Let F be a exponential (α, β)-metric of isotropic S-curvature on manifold M. In this paper,  a Lie sub-algebra of projective vector fields of a Finsler metric F is introduced denoted by SP(F). We classify SP(F) of isotropic S-curvature as a certain Lie sub-algebra of the Kiliing algebra k(M, α).

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References

1. H. Akbar-Zadeh, Champs de vecteurs projectifs sur le fibr´e unitaire , J. Math. Pure Appl. 65 (1986), 47–79.
2. H. Akbar-Zadeh, Sur les espaces de Finsler `a courbures sectionelles constantes, Acad. Roy. Belgian Bull. Cl. Sci. 74 (5) (1988), 281–322.
3. S. B`acs`o, X. Cheng and Z.Shen, Curvature properties of (α, β)-metrics, Advance. Stud. Pure. Math. 48(2007), 73–110.
4. M. Rafie-Rad and B. Rezaei, On the projective algebra of some (α, β)-metrics of isotropic S-curvature, Int. J. Geom. Methods Mod. Phys. 10 (2013) 048, 11 pp.
5. Z. Shen, Differential Geometry of Spray and Finsler Spaces (Kluwer Academic Publish-ers, 2001).
6. X. Mo, On the non-Riemannian quantity H of a Finsler metric, Diff. Geom. Appl. 27 (2009), 7–14.
7. B. Najafi, Z. Shen and A. Tayebi, Finsler metrics of scalar flag curvature with special non-Riemannian curvature properties, Geom. Dedicata 131 (2008), 87–98.
8. M. Rafie-Rad, Some new characterizations of projective Randers metrics with constant S-curvature, J. Geom. Phys. 9 (4) (2012), 272–278.
9. K. Yano, The Theory of Lie Derivatives and Its Applications (North Holland, Amster-dam, 1957).
10. S. Masoumi, Projective vector fields on special (α, β)-metric, J. Finsler Geom. Appl. 2 (2020), 83–93.
Journal of Finsler Geometry and its Applications
Volume 5, Issue 2
December 2024
Pages 1-13

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