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.

The flag curvature of the Numata Finsler structures is shown to admit a nontrivial prolongation to the one-dimensional case, revealing an unexpected link with the Schwarzian derivative of the diffeomorphisms associated with these Finsler structures. Mathematics Subject Classification 2000: 58B20, 53A55 1 Finsler structures in a nutshell 1.1 Finsler metrics A Finsler structure is a pair (M,F ) w...

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...

The paper introduces the approach to construction of the Lagrangian of the field (fields). This approach is based solely on the metric function of the Finsler space: the Lagrangian is constructed as the unit divided by the volume swept by the unit vector running through all the points of the indicatrix in the tangent space under the assumption of the tangent space being Euclidean. For the space...

In this paper we investigate the problem what kind of (two-dimensional) Finsler manifolds have a conformal change leaving the mixed curvature of the Berwald connection invariant? We establish a differential equation for such Finslerian energy functions and present the solutions under some simplification. As we shall see they are essentially the same as the singular Finsler metrics with constant...

1 We develop the method of anholonomic frames with associated nonlinear connection (in brief, N–connection) structure and show explicitly how geometries with local anisotropy (various type of Finsler–Lagrange–Cartan–Hamilton spaces) can be modelled on the metric–affine spaces. There are formulated the criteria when such generalized Finsler metrics are effectively defined in the Einstein, telepa...