Open Access
Research Article
Generalized second approximation Matsumoto metric
A. Soleimanasoliman@ju.edu.sa; amrsoleiman@yahoo.comDepartment of Mathematics Faculty of Science Al Jouf UniversitySkaka, Saudi ArabiaView full profile → , *S. G. ElgendiCorresponding authorselgendi@iu.edu.sa; salahelgendi@yahoo.comDepartment of Mathematics Faculty of Science Islamic University of MadinahBenha, Madinah, Saudi ArabiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 12 Apr 2024
- Published Online:
- 01 Nov 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDSGT-2024-005
- Pages:
- 65–85
Abstract
In this paper, we tackle a more general coordinate-free investigation of the second approximation Matsumoto metric. Specifically, we establish various geometric objects corresponding the second approximation Matsumoto metric L̃(x,y) = L + B + B2/L + B3/L2 in terms of the objects of L with a Finsler structure (M,L) and a one form B. Here we consider L is Finslerian and so we call L̃ the generalized second approximation Matsumoto metric. We describe the metric tensor of L̃ and its non-degeneracy. We limit the one form B to a one form associated with a concurent π-vector field in order to determine the geodesic spray, Barthel, and Berwald connections of L̃(x,y). Next, we compute the Barthel curvature of L̃.
Keywords
Subject Classifications
53C6053B4058B20
References
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