Journal of Finsler Geometry and its Applications
Volume:4 Issue: 2, Dec 2023

This paper is devoted to study of a class of conformally flat (α,β)-metrics that have of the form F = αexp(2s)/s; where s := β/α. They are called Kropina change of exponential (α,β)-metrics. We prove that if F has relatively isotropic mean Landsberg curvature or almost vanishing Xi-curvature then it is a Riemannian metric or a locally Minkowski metric. Also, we prove that, if F be a weak Einstein metric, then it is either a Riemannian metric or a locally Minkowski metric.

One of the Helmholtz conditions for the inverse problem of a ‎Lagrangian Mechanics is the metric compatibility of a semispray‎ ‎and the associated nonlinear connection with a generalized‎ ‎Lagrange metric‎. ‎In this paper‎, ‎with respect to the supermetric‎ ‎induced by the Hessian of the Lagrangian‎, ‎we find a family of‎ ‎nonlinear connections compatible with supermetric‎. ‎In a particular case‎, ‎when a Lagrangian superfunction‎ ‎is regular‎, ‎we have a solution for the Euler-Lagrange‎ ‎superequation which‎ ‎defines a metric nonlinear connection‎.

In the following text we show if D is Khalimsky line (resp. Khalimsky plane, Khalimsky circle, Khalimsky sphere), then for topological space X we show the collection of all quasicontinuous maps from D to X has cardinality card(X)ℵ.

The projective Ricci curvature is an important projective invariant in Finsler geometry. In this paper, we study and characterize projective Ricci flat isotropic S-curvature Randers metrics from a navigation data point of view and conclude that these metrics are weak Einsteinian.

In this paper we study the geometric properties of Finsler Σ-spaces . we prove that Infinite series Σ-spaces are Riemannian.

We present an algorithm for computing A-annihilated elements of the form QI[1] in H*QS0 where I runs through admissible sequences of positive excess. This is algorithm with polynomial time complexity to address a sub-problem of an unsolved problem in algebraic topology known as the hit problem of Peterson which is likely to be NP-hard.

This paper introduces new non-Riemannian quantities and classes of Finsler metrics. The study focuses on the class of Generalized Douglas Weyl GDW-metrics, which is contained in the class of Finsler metrics. The paper constructs the new sub-classes of GDW-metrics and presents illustrative examples.

In this paper, we remark some of the well-known curvature properties of square Finsler metrics. Then, we study weakly stretch square Finsler metrics.

In this paper, we investigate the mean Landsberg curvature of two subclasses of (α,β)-metrics. We prove that these subclasses of (α,β)-metrics with vanishing mean Landsberg curvature have vanishing S-curvature. Using it, we prove that these Finsler metrics are weakly Landsbergian if and only if they are Berwaldian.

In this paper, we consider invariant infinite series  (α, β)--metrics. Then we describe all geodesic vectors of this spaces on the left invariant hypercomplex four dimensional simply connected Lie groups.

The recurrence and birecurrence property in Finsler space have been studied by the Finslerian geometrics. The aim of this paper is to obtain the necessary and sufficient condition for Cartan’s second curvature tensor that is recurrnt and birecurrent in generalized BP−recurrent space and generalized BP−birecurrent space, respectively. We discuss certain identities belong to the mentioned spaces. Further, we end up this paper with some illustrative examples.

In this paper, we study reversibility of Riemann Curvature and Ricci curvature for the Ingarden-Támassy metric and prove two global results. First, we prove that a Ingarden-Támassy metric is R-reversible if and only if si = 0, sij|k = 0. Then we show that a Ingarden-Támassy metric is Ricci-reversible if and only if si = 0.