In this paper we study the sub-Finsler geometry as a time-optimal control problem. In particular, we consider non-smooth and non-strictly convex sub-Finsler structures associated with the Heisenberg, Grushin, and Martinet distributions. Motivated by problems in geometric group theory, we characterize extremal curves, discuss their optimality, and calculate the metric spheres, proving their Eucl...

Finsler and Lagrange spaces can be equivalently represented as almost Kähler manifolds endowed with a metric compatible canonical distinguished connection structure generalizing the Levi Civita connection. The goal of this paper is to perform a natural Fedosov– type deformation quantization of such geometries. All constructions are canonically derived for regular Lagrangians and/or fundamental ...

In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fields. We also prove that an L-reducible Finsler metric admitting a concurrent vector field reduces to a Landsberg metric.In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fi...

We prove the existence of optimal transport maps for the Monge problem when the cost is a Finsler distance on a compact manifold. Our point of view consists in considering the distance as a Mañé potential, and to rely on recent developments in the theory of viscosity solutions of the Hamilton-Jacobi equation. Résumé: On montre l’existence d’une application de transport optimale pour le problème...

These Smarandache spaces are right theories for objectives by logic. However, the mathematical combinatorics is a combinatorial theory for branches in classical mathematics motivated by a combinatorial speculation. Both of them are unifying theories for sciences and contribute more and more to mathematics in the 21st century. In this paper, I introduce these two subjects and mainly concentrate ...

In this paper is studied the differential geometry of the complex indicatrix, which is approached as an embedded CR hypersurface of the punctual holomorphic tangent bundle of a complex Finsler space. Following the study of CR submanifolds of a Kähler manifold and using the submanifold formulae there are investigated some properties of the complex indicatrix, such as the fact that it is an extri...

a projective parameter of a geodesic as solution of certain ode is defined to be a parameter which is invariant under projective change of metric. using projective parameter and poincaré metric, an intrinsic projectively invariant pseudo-distance can be constructed. in the present work, solutions of the above ode are characterized with respect to the sign of parallel ricci tensor on a finsler s...

Locally flat Finsler metrics arise from information geometry. Some speciel locally dually flat Finsler metrics had been studied in Cheng et al. [3] and Xia [4] respectively. As we konw, a new class of Finsler metrics called general (α, β)-metrics are introduced, which are defined by a Riemannian metrics α and 1-form β. These metrics generalize (α, β)-metrics naturally. In this paper, we give a ...

In this paper, we study homogeneous geodesics in homogeneous Finsler spaces. We first give a simple criterion that characterizes geodesic vectors. We show that the geodesics on a Lie group, relative to a bi-invariant Finsler metric, are the cosets of the one-parameter subgroups. The existence of infinitely many homogeneous geodesics on compact semi-simple Lie group is established. We introduce ...

In the present paper, we investigate the necessary and sufficient condition of a given Finsler metric to be Einstein. The considered Einstein Finsler metric in the study describes all different kinds of Einstein metrics which are pointwise projective to the given one.