Zoltán Muzsnay

PROJECTIVE AND FINSLER METRIZABILITY: PARAMETERIZATION-RIGIDITY OF THE GEODESICS

In this work we show that for the geodesic spray

Variational Principles For Second-Order Differential Equations: Application of the Spencer Theory to Characterize Variational Sprays

S

FINSLER METRIZABLE ISOTROPIC SPRAYS AND HILBERT’S FOURTH PROBLEM

of a Finsler function

An invariant variational principle for canonical flows on Lie groups

F

Sprays metrizable by Finsler functions of constant flag curvature

the most natural projective deformation

Characterization of projective Finsler manifolds of constant curvature having infinite dimensional holonomy group

\widetilde{S}=S -2 \lambda F\mathbb C

Holonomy Theory of Finsler Manifolds

leads to a non-Finsler metrizable spray, for almost every value of

On the projective Finsler metrizability and the integrability of Rapcsák equation

\lambda \in \mathbb R

Invariant Metrizability and Projective Metrizability on Lie Groups and Homogeneous Spaces

. This result shows how rigid is the metrizablility property with respect to certain reparameterizations of the geodesics. As a consequence we obtain that the projective class of an arbitrary spray contains infinitely many sprays that are not Finsler metrizable.

Non-existence of Funk functions for Finsler spaces of non-vanishing scalar flag curvature

An introduction to formal integrability theory of partial differential systems Frolicher-Nijenhuis theory of derivations differential algebraic formalism of connections necessary conditions for variational sprays obstructions to the integrability of the Euler-Lagrange system the classification of locally variational sprays on two-dimensional manifolds Euler-Lagrange systems in the isotropic case.