On Ξ-curvature of m-th root Finsler metrics

Articles in Press

Document Type : Original Article

Authors

1 Department of Mathematics, Basic Sciences Faculty University of Bonab, Bonab, Iran

2 Department of Mathematics, Basic Sciences Faculty University of Bonab, Bonab, Iran.

Abstract

The notions of S-curvature and Ξ-curvature introduced by Shen that is very
effective for understanding the other Riemannian and non-Riemannian geometric properties
of Finsler metrics. Here, we study the S-curvature and Ξ-curvature of the class of cubic
and quartic (α, β)-metrics. We prove that third root (α, β)-metric of vanishing Ξ-curvature
reduces to a (−1/3)-Kropina metric or it has vanishing S-curvature. Then, we prove that
quartic (α, β)-metric of vanishing Ξ-curvature reduces to a special form of quartic (α, β)-
metric or it has vanishing S-curvature.

Keywords

References

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Journal of Finsler Geometry and its Applications

Articles in Press, Accepted Manuscript
Available Online from 08 August 2025

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