Abstract
Geodesics represent the shortest path between two points in curved spacetime and are vital in the study of Finsler manifolds. Matsumoto and Park first derived the geodesic equation as a secondorder differential equation in a two-dimensional Finsler manifold with Randers, Kropina, and Matsumoto metrics. Building on this foundation, our paper presents the geodesic differential equation for a two-dimensional Finsler manifold using a special cubic power metric. In this two-dimensional setting, this work also looks at certain well-known geometric curves and analyzes their variants as solutions to the geodesic differential equation. Additionally, this work examines the geometric applications of the geodesic’s nonlinear differential equations on catenoids, cylinders, spheres, and pseudo-spheres. These results enhance the study of curvature, anisotropy, and structural characteristics in Finsler geometry and offer a deeper understanding of the geometric and physical behavior of Finsler spaces with special cubic power metrics. The findings may find use in advanced surface modeling, theoretical physics, and geometrical analysis.
Recommended Citation
Prajapati, Sejal; Tripathi, Brijesh Kumar; and Chaubey, V. K.
(2026).
(SI16 No06) Equations of Geodesics in Two-dimensional Finsler Manifold with a Special Cubic (α, β)-Metric,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 21,
Iss.
3, Article 4.
Available at:
https://digitalcommons.pvamu.edu/aam/vol21/iss3/4