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Elgendi, Salah, Soleiman, Amr. (1405). On generalized silver Finsler metrics. سامانه مدیریت نشریات علمی, 7(1), 103-122. doi: 10.22098/jfga.2025.17873.1170
Salah Gomaa Elgendi; Amr Soleiman. "On generalized silver Finsler metrics". سامانه مدیریت نشریات علمی, 7, 1, 1405, 103-122. doi: 10.22098/jfga.2025.17873.1170
Elgendi, Salah, Soleiman, Amr. (1405). 'On generalized silver Finsler metrics', سامانه مدیریت نشریات علمی, 7(1), pp. 103-122. doi: 10.22098/jfga.2025.17873.1170
Elgendi, Salah, Soleiman, Amr. On generalized silver Finsler metrics. سامانه مدیریت نشریات علمی, 1405; 7(1): 103-122. doi: 10.22098/jfga.2025.17873.1170

On generalized silver Finsler metrics

Journal of Finsler Geometry and its Applications
دوره 7، شماره 1، 2026، صفحه 103-122    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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