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...

In the present paper we submit for study a new class of Finsler spaces. Through restricting the homogeneity condition from the definition of a complex Finsler metric to real scalars, λ ∈ R, is obtained a wider class of complex spaces, called by us the R−complex Finsler spaces. Two subclasses are taken in consideration: the Hermitian and the non-Hermitian R−complex Finsler spaces. In an R−comple...

Adopting the pullback approach to Finsler geometry, the aim of the present paper is to provide intrinsic (coordinate-free) proofs of the existence and uniqueness theorems for the Chern (Rund) and Hashiguchi connections on a Finsler manifold. To accomplish this, we introduce and investigate the notions of semispray and nonlinear connection associated with a given regular connection, in the pullb...

The Chern–Rund connection from Finsler geometry is settled in the generalized Lagrange spaces. For the geometry of these spaces, we refer to [5]. Mathematics Subject Classification: 53C60

In this paper we obtain the conditions in which two complex Finsler metrics are projective, i.e. have the same geodesics as point sets. Two important classes of such metrics are submitted to our attention: conformal projective and weakly projective complex Finsler spaces. For each of them we study the transformations of the canonical connection. We pay attention for local projectivity with a pu...

The work extends the A. Connes’ noncommutative geometry to spaces with generic local anisotropy. We apply the E. Cartan’s anholonomic frame approach to geometry models and physical theories and develop the nonlinear connection formalism for projective module spaces. Examples of noncommutative generation of anholonomic Riemann, Finsler and Lagrange spaces are analyzed. We also present a research...

The present paper deals with an intrinsic investigation of the notion of a concurrent π-vector field on the pullback bundle of a Finsler manifold (M,L). The effect of the existence of a concurrent π-vector field on some important special Finsler spaces is studied. An intrinsic investigation of a particular β-change, namely the energy β-change (L̃(x, y) = L(x, y) + B(x, y)with B := g(ζ, η); ζ bei...

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...