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The projective Finsler metrizability problem deals with the question whether a projective-equivalence class of sprays is the geodesic class of a (locally or globally defined) Finsler function. In this paper we use Hilbert-type forms to state a number of different ways of specifying necessary and sufficient conditions for this to be the case, and we show that they are equivalent. We also address several related issues of interest including path spaces, Jacobi fields, totally-geodesic submanifolds of a spray space, and the equivalence of path geometries and projective-equivalence classes of sprays.
In this paper, we first give two fundamental principles under a technique to characterize conformal vector fields of $(alpha,beta)$ spaces to be homothetic and determine the local structure of those homothetic fields. Then we use the principles to st
An $(alpha,beta)$-manifold $(M,F)$ is a Finsler manifold with the Finsler metric $F$ being defined by a Riemannian metric $alpha$ and $1$-form $beta$ on the manifold $M$. In this paper, we classify $n$-dimensional $(alpha,beta)$-manifolds (non-Rander
An $(alpha,beta)$-metric is defined by a Riemannian metric and $1$-form. In this paper, we investigate the known characterization for $(alpha,beta)$-metrics of isotropic S-curvature. We show that such a characterization should hold in dimension $nge
A systematic development of the so-called Palatini formalism is carried out for pseudo-Finsler metrics $L$ of any signature. Substituting in the classical Einstein-Hilbert-Palatini functional the scalar curvature by the Finslerian Ricci scalar constr
An $(alpha,beta)$-metric is defined by a Riemannian metric $alpha$ and $1$-form $beta$. In this paper, we study a known class of two-dimensional $(alpha,beta)$-metrics of vanishing S-curvature. We determine the local structure of those metrics and sh