A geometric procedure is elaborated for transforming (pseudo) Riemanian metrics and connections into canonical geometric objects (metric and nonlinear and linear connections) for effective Lagrange, or Finsler, geometries which, in their turn, can be equivalently represented as almost Kähler spaces. This allows us to formulate an approach to quantum gravity following standard methods of deforma...

In this paper we prove several multiplicity results of t-periodic light rays in conformally stationary spacetimes using the Fermat metric and the extensions of the classical theorems of Gromoll-Meyer and Bangert-Hingston to Finsler manifolds. Moreover, we exhibit some stationary spacetimes with a finite number of t-periodic light rays and compute a lower bound for the period of the light rays w...

Abstract Finsler geometry is a natural arena to investigate the physics of spacetimes with local Lorentz violation. The directional dependence metric provides way encode Lorentz-violating effects into geometric structure spacetime. Here, classical field theory proposed in special geometry, so-called Randers-Finsler spacetime, where violation produced by background vector field. By promoting dif...

In Theorem 1, we generalize some results of Szabó [Sz1, Sz2] for Berwald metrics that are not necessarily strictly convex: we show that for every Berwald metric F there always exists a Riemannian metric affine equivalent to F . As an application we show (Corollary 3) that every Berwald projectively flat metric is a Minkowski metric; this statement is a “Berwald” version of Hilbert’s 4th problem...

Let x : (M, F ) →֒ (V n+1, F ) be a simply connected hypersurface in a Minkowski space (V n+1, F ). In this paper, using the Gauss formula of Chern connection on Finsler submanifolds, we shall prove that if x(p) is normal to Tp(M)(∀p ∈ M), then M with the induced metric is isometric to the standard Euclidean sphere.

We generalize the Zermelo navigation on Riemannian manifolds (M,h), admitting a space dependence of a ship's speed 0 < |u(x)|h ≤ 1 in the presence of a perturbation W̃ determined by a strong (critical) velocity vector eld satisfying |W̃ (x)|h = |u(x)|h, with application of Finsler metric of Kropina type.

In this paper, we construct a framed f -structure on the slit tangent space of a Rizza manifold. This induces on the indicatrix bundle an almost contact metric. We find the conditions under which this structure reduces to a contact or to a Sasakian structure. Finally we study these structures on Kählerian Finsler manifolds. M.S.C. 2010: 53B40, 53C60, 32Q60, 53C15.

A general framework for the description of classic wave propagation is introduced. This relies on a cone structure C determined by an intrinsic space ? velocities (point, direction and time-dependent) observers’ vector field ???t whose integral curves provide both Zermelo problem auxiliary Lorentz–Finsler metric G compatible with C. The PDE wavefront reduced to ODE t-parametrized geodesics Part...

Abstract A relevant property of equifocal submanifolds is that their parallel sets are still immersed submanifolds, which makes them a natural generalization the so-called isoparametric submanifolds. In this paper, we prove regular fibers an analytic map π : M m+k → B k whenever endowed with complete Finsler metric and there restriction submersion for certain on image. addition, when provide si...