A new hypersurface of Tzitzeica type is obtained in all three forms: parametric, implicit and explicit. To a two-parameters family of cubic Tzitzeica surfaces we associate a cubic Finsler function for which the regularity is expressed as the non-flatness of the Tzitzeica indicatrix. A natural relationship is obtained between cubic Tzitzeica surfaces and three-dimensional Berwald spaces with cub...

We investigate existence and uniqueness of p-means ep and the median e1 of a probability measure μ on a Finsler manifold, in relation with the convexity of the support of μ. We prove that ep is the limit point of a continuous time gradient flow. Under some additional condition which is always satisfied for p ≥ 2, a discretization of this path converges to ep. This provides an algorithm for dete...

Let Ω be a domain in a smooth complete Finsler manifold, and let G be the largest open subset of Ω such that for every x in G there is a unique closest point from ∂Ω to x (measured in the Finsler metric). We prove that the distance function from ∂Ω is in C k,α loc (G ∪ ∂Ω), k ≥ 2 and 0 < α ≤ 1, if ∂Ω is in C k,α .

We revisit the physical arguments which lead to definition of stress-energy tensor $T$ in Lorentz-Finsler setting $(M,L)$ starting at classical Relativity. Both standard heuristic approach using fluids and Lagrangian one are taken into account. In particular, we argue that Finslerian breaking Lorentz symmetry makes an anisotropic 2-tensor (i. e., a for each $L$-timelike direction), contrast wit...

We study non-reversible Finsler metrics with constant flag curvature 1 on S and show that the geodesic flow of every such metric is conjugate to that of one of Katok’s examples, which form a 1-parameter family. In particular, the length of the shortest closed geodesic is a complete invariant of the geodesic flow. We also show, in any dimension, that the geodesic flow of a Finsler metrics with c...

We consider an optimization problem related to mass transportation: given two probabilities f and f− on an open subset Ω ⊂ R , we let vary the cost of the transport among all distances associated with conformally flat Riemannian metrics on Ω which satisfy an integral constraint (precisely, an upper bound on the L-norm of the Riemannian coefficient). Then, we search for an optimal distance which...

The present paper is a continuation of the foregoing paper [16]. The main aim is to establish an intrinsic investigation of the conformal change of the most important special Finsler spaces. Necessary and sufficient conditions for such special Finsler manifolds to be invariant under a conformal change are obtained. Moreover, the conformal change of Chern and Hashiguchi connections, as well as t...

‎the notion of quasi-einstein metric in physics is equivalent to the notion of ricci soliton in riemannian spaces‎. ‎quasi-einstein metrics serve also as solution to the ricci flow equation‎. ‎here‎, ‎the riemannian metric is replaced by a hessian matrix derived from a finsler structure and a quasi-einstein finsler metric is defined‎. ‎in compact case‎, ‎it is proved that the quasi-einstein met...

The equivalence problem for control systems under non-linear feedback is recast as a problem involving the determination of the invariants of submanifolds in the tangent bundle of state space under fiber preserving transformations. This leads to a fiber geometry described by the invariants of submanifolds under the general linear group, which is the classical subject of centro-affine geometry. ...