Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a non degenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange geometry. In this paper, we study a generalization, which consists of replacing the tangent bundle by a general tangent manifold, and the Lagrangian by a fami...

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...

Abstract We prove a normal form for contact forms close to Zoll one and deduce that on any closed manifold are local maximizers of the systolic ratio. Corollaries this result are: (1) sharp inequalities Riemannian Finsler metrics ones, (2) perturbative case conjecture Viterbo symplectic capacity convex bodies, (3) generalization Gromov’s non-squeezing theorem in intermediate dimensions symplect...

Given the class of Finsler spaces with Lorentzian signature [Formula: see text] on a manifold endowed timelike vector field satisfying at any point slit tangent bundle, pseudo-Riemannian metric defined is associated to fundamental tensor text]. Furthermore, an affine, torsion free connection Chern determined by The definition average does not make use Therefore, there no direct relation between...

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...

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...

Abstract We study an action integral for Finsler gravity obtained by pulling back Einstein-Cartan-like Lagrangian from the tangent bundle to base manifold. The vacuum equations are imposing stationarity with respect any section (observer) and well posed as they independent of section. They imply that in metric is actually velocity variable so dynamics becomes coincident general relativity.

The broken scattering relation consists of the total lengths geodesics that start from boundary, change direction once inside manifold, and propagate to boundary. We show if two reversible Finsler manifolds satisfying a convex foliation condition have same relation, then they are isometric. This implies some anisotropic material parameters Earth can be in principle reconstructed single measurem...

Let $$(X,\omega )$$ be a Kähler manifold and $$\psi : \mathbb R \rightarrow R_+$$ concave weight. We show that $${\mathcal {H}}_\omega $$ admits natural metric $$d_\psi whose completion is the low energy space {E}}_\psi , introduced by Guedj–Zeriahi. As not induced Finsler metric, main difficulty to triangle inequality holds. study properties of resulting complete $$({\mathcal ,d_\psi .

The geometries of higher order, defined in the present paper as the study of the category of jet bundles (J o M, π,M), were suggested by the old problem of the prolongations to J o M of Riemannian structures g apriori given on the base manifold M. In the case k = 1 there are very good examples: the geometry of Finsler spaces and the geometry of Lagrange spaces, [3]. For k > 1 there are some geo...