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...

We determine a 2-codimensional CR-structure on the slit tangent bundle T0M of a Finsler manifold (M, F) by imposing a condition on the almost complex structure associated to F when restricted to the structural distribution of a framed f -structure. This condition is satisfied when (M, F) is of scalar flag curvature (particularly flat). In the Riemannian case (M, g) this last condition means tha...

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...

In a series of papers ([2, 3, 4]) the relations existing between the metric properties of Randers spaces and the conformal geometry of stationary Lorentzian manifolds were discovered and investigated. These relations were called in [4] Stationary-to-Randers Correspondence (SRC). In this paper we focus on one aspect of SRC, the equality between the index of a geodesic in a Randers space and that...