We study a special class of Finsler metrics which we refer to as Almost Rational (shortly, AR-Finsler metrics). give necessary and sufficient conditions for an manifold (M, F) be Riemannian. The rationality some geometric objects such Cartan torsion, geodesic spray, Landsberg curvature S-curvature is investigated. For particular subfamily have proved that if F has isotropic S-curvature, then th...

In 1977, M. Matsumoto and R. Miron [9] constructed an orthonormal frame for an n-dimensional Finsler space, called ‘Miron frame’. The present authors [1, 2, 3, 10, 11] discussed four-dimensional Finsler spaces equipped with such frame. M. Matsumoto [7, 8] proved that in a three-dimensional Berwald space, all the main scalars are h-covariant constants and the h-connection vector vanishes. He als...

We give a new and complete proof of the following theorem, discovered by Detlef Laugwitz: (forward) complete and connected finite dimensional Finsler manifolds admitting a proper homothety are Minkowski vector spaces. More precisely, we show that under these hypotheses the Finsler manifold is isometric to the tangent Minkowski vector space of the fixed point of the homothety via the exponential...

Abstract. The aim of this paper is to consider Busemann-type inequalities on Finsler manifolds. We actually formulate a rigidity conjecture: any Finsler manifold which is a Busemann NPC space is Berwaldian. This statement is supported by some theoretical results and numerical examples. The presented examples are obtained by using evolutionary techniques (genetic algorithms) which can be used fo...

Following the study on volume of indicatrices in a real Finsler space, in this paper we are investigating some volume properties of the indicatrix considered in an arbitrary fixed point of a complex Finsler manifold. Since for each point of a complex Finsler space the indicatrix is an embedded CR-hypersurface of the punctured holomorphic tangent bundle, by means of its normal vector, the volume...

here, a finsler manifold $(m,f)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. certain subspaces of the tangent spaces of $m$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. it is shown that if the dimension of foliation is constant, then the distribution is involutive a...

Our main observation concerns closed geodesics on surfaces M with a smooth Finsler metric, i.e. a function F : TM → [0,∞) which is a norm on each tangent space TpM , p ∈ M , which is smooth outside of the zero section in TM , and which is strictly convex in the sense that Hess(F ) is positive definite on TpM \ {0}. One calls a Finsler metric F symmetric if F (p,−v) = F (p, v) for all v ∈ TpM . ...

Asking that the metric of a complex Finsler space should be strong convex, Abate and Patrizio ([1]) associate to the real tangent bundle a real Finsler metric for which they analyze the relation between Cartan (real) connection of the obtained space and the real image of Chern-Finsler complex connection. Following the same ideas, in the present paper we shall deal with the more general case of ...