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On generalized silver Finsler metrics | ||
| Journal of Finsler Geometry and its Applications | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 26 آبان 1404 اصل مقاله (364.94 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22098/jfga.2025.17873.1170 | ||
| نویسندگان | ||
| Salah Gomaa Elgendi* 1؛ Amr Soleiman2 | ||
| 1Department of Mathematics, College of Science, Jouf University, Skaka, KSA | ||
| 2Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, KSA | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Silver Finsler metric؛ Geodesic spray؛ Barthel connection؛ Berwald connection | ||
| مراجع | ||
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