The well-known invariants of conics are computed for classes of Finsler and Lagrange spaces. For the Finsler case, some (α, β)-metrics namely Randers, Kropina and ”Riemann”-type metrics provides conics as indicatrices and a Randers-Funk metric on the unit disk is treated as example. The relations between algebraic and differential invariants of (α, β)-metrics are pointed out as a method to use ...

equality of -curvatures of the berwald and cartan connections leads to a new class of finsler metrics, so-called bc-generalized landsberg metrics. here, we prove that every bc-generalized landsberg metric of scalar flag curvature with dimension greater than two is of constant flag curvature.

The dual flatness for Riemannian metrics in information geometry has been extended to Finsler metrics. The aim of this paper is to study the dual flatness of the so-called (α, β)-metrics in Finsler geometry. By doing some special deformations, we will show that the dual flatness of an (α, β)-metric always arises from that of some Riemannian metric in dimensional n ≥ 3.

The concept of locally dually flat Finsler metrics originate from information geometry. As we know, (α, β)-metrics defined by a Riemannian metric α and an 1-form β, represent an important class of Finsler metrics, which contains the Matsumoto metric. In this paper, we study and characterize locally dually flat first approximation of the Matsumoto metric with isotropic S-curvature, which is not ...

The notion of dually flat Finsler metrics arise from information geometry. In this paper, we will study a special class of Finsler metrics called Randers metrics to be dually flat. A simple characterization is provided and some non-trivial explicit examples are constructed. In particular, We will show that the dual flatness of a Randers metric always arises from that of some Riemannian metric b...

One of the key properties of the length of a curve is its lower semicontinuity : if a sequence of curves γi converges to a curve γ, then length(γ) ≤ lim inf length(γi). Here the weakest type of pointwise convergence suffices. There are higher-dimensional analogs of this semicontinuity for Riemannian (and even Finsler) metrics. For instance, the Besicovitch inequality (see, e.g., [1] and [4]) im...

This article is an exposition of four loosely related remarks on the geometry of Finsler manifolds with constant positive flag curvature. The first remark is that there is a canonical Kähler structure on the space of geodesics of such a manifold. The second remark is that there is a natural way to construct a (not necessarily complete) Finsler n-manifold of constant positive flag curvature out ...

Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a non degenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange geometry. In this paper, we study a generalization, which consists of replacing the tangent bundle by a general tangent manifold, and the Lagrangian by a fami...

The notion of isometric submersion is extended to Finsler spaces and it is used to construct examples of Finsler metrics on complex and quaternionic projective spaces all of whose geodesics are (geometrical) circles.