Abstract In this paper, we study locally projectively flat Finsler metrics of constant flag curvature. We find equations that characterize these by warped product. Using the obtained equations, manufacture new product vanishing These contain metric introduced Berwald and spherically symmetric given Mo-Zhu.

In this paper, we establish a closer relation between the Berwald scalar curvature and [Formula: see text]-curvature. fact, prove that Finsler metric has isotropic if only it weakly For metrics of flag text]-curvature, they have almost text]-curvature is isotropic.

We study a relation between certain extensions of the Clifford bundle and Finsler type structures that naturally generalize standard (pseudo)-Riemannian metric Dirac matrices. show for flat metrics there is triangle map constructed from [Formula: see text]-forms on text], extension relevant operators.

In a previous paper [Barceló C et al 2001 Class. Quantum Grav. 18 3595– 610 (Preprint gr-qc/0104001)] we have shown that the occurrence of curved spacetime ‘effective Lorentzian geometries’ is a generic result of linearizing an arbitrary classical field theory around some nontrivial background configuration. This observation explains the ubiquitous nature of the ‘analogue models’ for general re...

The purpose of this work is to extend the formalism of stochastic calculus to the case of spaces with local anisotropy (modeled as vector bundles with compatible nonlinear and distinguished connections and metric structures and containing as particular cases different variants of Kaluza–Klein and generalized Lagrange and Finsler spaces). We shall examine nondegenerate diffusions on the mentione...

After defining what is meant by a complex spray X on a complex manifold M , we introduce the notion of a spray complex curve associated to X. Several equivalent formulations are derived and we give necessary and sufficient conditions for M to admit spray complex curves for X through each point and in each direction. Refinements of this result are then derived for some special cases, for example...

We consider a natural mechanical system on Finsler manifold and study its curvature using the intrinsic Jacobi equations (called curves) along extremals of least action system. The for such is expressed in terms Riemann Chern (involving gradient potential) Hessian potential w.r.t. Riemannian metric induced from metric. As an application, we give sufficient conditions Hamiltonian flows to be hyp...

In this paper we investigate the spectral problem in Finsler geometry. Due to nonlinearity of Finsler–Laplacian operator, introduce faithful dimension pairs by means which spectrum a compact reversible metric measure manifold is defined. Various upper and lower bounds such eigenvalues are provided spirit Cheng, Buser Gromov, extend several aspects results Hassannezhad, Kokarev Polterovich. More...