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...

Let M be a compact simply connected manifold satisfying H⁎(M;Q)≅Td,n+1(x) for integers d≥2 and n≥1. If all prime closed geodesics on (M,F) with an irreversible bumpy Finsler metric F are elliptic, then either there exist exactly dn(n+1)2 (when is even) or (d+1) d≥3 odd) distinct geodesics, infinitely many geodesics.

Abstract In this paper, we study a singular Finsler double phase problem with nonlinear boundary condition and perturbations that have type of critical growth, even on the boundary. Based variational methods in combination truncation techniques, prove existence at least one weak solution for under very general assumptions. Even case when manifold reduces to Euclidean norm, our work is first dea...

A linear connection on a Finsler manifold is called compatible to the function if its parallel transports preserve Finslerian length of tangent vectors. Generalized Berwald manifolds are equipped with connection. In paper we present general and intrinsic method characterize connections dimension three. We prove that not unique then indicatrices must be Euclidean surfaces revolution. The surplus...

In this work, we study the set of strictly accretive matrices, that is, matrices with positive definite Hermitian part, and show can be interpreted as a smooth manifold. Using recently proposed symmetric polar decomposition for sectorial manifold is diffeomorphic to direct product (Hermitian) unitary matrices. Utilizing decomposition, introduce family Finsler metrics on characterize their geode...

In this paper we extend the study of the indicatrix of a complex Finsler space initiated in [10, 11]. The equations that can be introduced on the indicatrix, which is studied as a hypersurface of a complex Finsler space, are investigated. In this manner, using the equations of Gauss-Weingarten, the link between the intrinsic and induced connection is deduced. The equations of Gauss, H -and A-Co...

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...

Given a compact Kahler manifold, the space $\mathcal H$ of its (relative) potentials is an infinite dimensional Frechet on which Mabuchi and Semmes have introduced natural connection $\nabla$. We study certain Lagrangians $T\mathcal H$, in particular Finsler metrics, that are parallel with respect to connection. show geodesics $\nabla$ paths least action, prove convexity property action. This g...