On generalized silver Finsler metrics

Articles in Press

Document Type : Original Article

Authors

1 Department of Mathematics, College of Science, Jouf University, Skaka, KSA

2 Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, KSA

Abstract

In this paper, we present a coordinate-free investigation of the generalized silver Finsler metric. Specifically, for a Finsler manifold (M, L)$and a 1-form B, we study various geometric structures associated with the Finsler metric L∼= L ∅(s), where ∅(s):= s2 - 2s - 1.The function ∅(s) has roots s1 = 1 - √2 and s2 = 1 +√2, where the positive root represents the so-called the silver ratio. Assuming that L is a Finsler metric, we refer to L∼ as the generalized silver Finsler metric. We derive the associated metric and Cartan tensors, along with other fundamental geometric objects. The non-degeneracy condition of the metric tensor of L∼ is characterized. We compute the geodesic spray, Barthel connection, and Berwald connection of L∼, when the 1-form B arises from a concurrent π-vector field. Furthermore, we determine the curvature of the Barthel connection associated with L∼. An illustrative example is also provided.

Keywords

References

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Journal of Finsler Geometry and its Applications

Articles in Press, Accepted Manuscript
Available Online from 17 November 2025

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