In this paper, we study a special class of generalized Douglas-Weyl metrics whose Douglas curvature is constant along any Finslerian geodesic. We prove that for every Landsberg metric in this class of Finsler metrics, ? = 0 if and only if H = 0. Then we show that every Finsler metric of non-zero isotropic flag curvature in this class of metrics is a Riemannian if and only if ? = 0.

Gravitational field equations in Randers-Finsler space of approximate Berwald type are investigated. A modified Friedmann model is proposed. It is showed that the accelerated expanding universe is guaranteed by a constrained RandersFinsler structure without invoking dark energy. The geodesic in Randers-Finsler space is studied. The additional term in the geodesic equation acts as repulsive forc...

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...

A complex Finsler metric is an upper semicontinuous function F : T 1,0 M → R + defined on the holomorphic tangent bundle of a complex Finsler manifold M , with the property that F (p; ζv) = |ζ|F (p; v) for any (p; v) ∈ T 1,0 M and ζ ∈ C. Complex Finsler metrics do occur naturally in function theory of several variables. The Kobayashi metric introduced in 1967 ([K1]) and its companion the Carath...

Modern gauge theories of high energy physics, investigations in classical and quantum gravity and recent unifications of superstring theories (the so–called M– F– and S– theories) are characterized by a large application of geometric and topological methods. There are elaborated a number of Kaluza–Klein models of space–time and proposed different variants of compactification of higher dimension...

The metrizability of sprays, particularly symmetric linear connections, is studied in terms of semi-basic 1-forms using the tools developed by Bucataru and Dahl in [2]. We introduce a type of metrizability in relationship with the Finsler and projective metrizability. The Lagrangian corresponding to the Finsler metrizability as well as the Bucataru–Dahl characterization of Finsler and projectiv...

In this paper we prove that the holonomy group of a simply connected locally projectively flat Finsler manifold of constant curvature is a finite dimensional Lie group if and only if it is flat or it is Riemannian. In particular, the holonomy group of non-Riemannian projective Finsler manifolds of nonzero constant curvature is infinite dimensional.

The pullback approach to global Finsler geometry is adopted. Three classes of recurrence in Finsler geometry are introduced and investigated: simple recurrence, Ricci recurrence and concircular recurrence. Each of these classes consists of four types of recurrence. The interrelationships between the different types of recurrence are studied. The generalized concircular recurrence, as a new conc...

The aim of this paper is to produce new examples of Riemannian and Finsler structures having as model a scalar deformation of conics inspired by the scaling transformation. It continues [4] from the point of view of relationship between quadratic polynomials (which provide equations of conics in dimension 2) and Finsler geometries. A type of Finslerian flow is introduced, based on the previous ...