A Finsler space (M,Σ) is said to be geodesically reversible if each oriented geodesic can be reparametrized as a geodesic with the reverse orientation. A reversible Finsler space is geodesically reversible, but the converse need not be true. In this note, building on recent work of LeBrun and Mason [13], it is shown that a geodesically reversible Finsler metric of constant flag curvature on the...

We present a gravitational quantum dynamics theory that combines field for particle in space-time with classical Einstein’s general relativity non-Riemannian Finsler space. This approach is based on the geometrization of mechanics proposed Tavernelli (Ann. Phys. 371:239, 2016) and effects into global curvature space induced by potential associated to matter fields. In order make this compatible...

Any Riemannian manifold has a canonical collection of valuations (finitely additive measures) attached to it, known as the intrinsic volumes or Lipschitz–Killing valuations. They date back remarkable discovery H. Weyl that coefficients tube volume polynomial are invariants metric. As consequence, behave naturally under isometric immersions. This phenomenon, subsequently observed in number diffe...

This paper is devoted to a study of geodesics of Finsler metrics via Zermelo navigation. We give a geometric description of the geodesics of the Finsler metric produced from any Finsler metric and any homothetic field in terms of navigation representation, generalizing a result previously only known in the case of Randers metrics with constant S-curvature. As its application, we present explici...

Minkowski’s second theorem can be stated as an inequality for n-dimensional flat Finsler tori relating the volume and minimal product of lengths closed geodesics which form a homology basis. In this paper we show how fundamental result promoted to principle holding larger class manifolds. This includes manifolds first Betti number dimension do no necessarily coincide, prime example being case s...

These days we can get massive information and it is hard to deal with it without computers. Machine learning is effective for computers to manage massive information. Machine learning uses various learning machine models, for instance, decision trees, Bayesian Networks, Support Vector Machine, Hidden Markov Model, normal mixed distributions, neural networks and so on. Some of them are stochasti...

In this paper we study the two-dimensional complex Finsler spaces with (α, β)-metrics by using the complex Berwald frame. A special approach is dedicated to the complex Berwald spaces with (α, β) metrics. We establish the necessary and sufficient condition so that the complex Randers and Kropina spaces should be complex Berwald spaces, and we will illustrate the existence of these spaces in som...