Finsler geometry is a generalization of Riemannian geometry that allows the length of a curve to be defined by an arbitrary function of the tangent vector, rather than by a quadratic form. A Finsler space is a manifold equipped with such a length function, called a Finsler metric¹.
Three dimensional Finsler spaces are Finsler spaces of dimension three. They have applications in various fields of mathematics and physics, such as differential geometry, dynamical systems, relativity theory, and cosmology²³.
Some examples of applications of three dimensional Finsler spaces are:
- The study of geodesics and curvature properties of Finsler spaces, such as C-reducible, semi C-reducible, P-reducible, L-reducible, and S3-like or S4-like Finsler spaces² .
- The classification and characterization of homogeneous and left-invariant Finsler metrics on Lie groups and symmetric spaces² .
- The investigation of special classes of Finsler metrics, such as Matsumoto metrics, Randers metrics, cubic metrics, fourth root metrics, and generalized symmetric metrics² .
- The exploration of the connections between Finsler geometry and relativity theory, such as the equivalence principle, the gravitational field equations, the cosmological models, and the gravitational lensing³ .
(1) P∗- Reducible Finsler Spaces and Applications - SSRN. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3090361.
(2) Jourrnal of Finsler geometry and its Applications - Google Scholar. https://scholar.google.com/citations?user=beZpfskAAAAJ.
(3) -REDUCIBLE FINSLER SPACES AND APPLICATIONS - SSRN. https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID3090361_code2148259.pdf?abstractid=3090361&mirid=1.
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