José Barbosa Gomes | Searcharxiv

arXiv2026

On rigidity of Finsler manifolds without conjugate points and with constant $S$-curvature

We study rigidity phenomena in closed Finsler manifolds without conjugate points under assumptions on the $S$-curvature. We prove that a closed $C^ω$ Finsler manifold with constant $S$-curvature, continuous Green bundles, and admitting a hyperbolic closed geodesic must be Riemannian. In the $C^\infty$ setting, the same conclusion holds under the additional assumption that the geodesic flow is transitive. As a consequence, we obtain rigidity results for Finsler manifolds with uniform visibility universal covering. Our approach is based on the analysis of the Cartan vector field as a Jacobi field and its interaction with the geometry of Green bundles.

math.DG↗

arXiv2018

Periodic Solutions of Hilbert's Fourth Problem

It is shown that a possibly irreversible $C^2$ Finsler metric on the torus, or on any other compact Euclidean space form, whose geodesics are straight lines is the sum of a flat metric and a closed $1$-form. This is used to prove that if $(M,g)$ is a compact Riemannian symmetric space of rank greater than one and $F$ is a {\sl reversible} $C^2$ Finsler metric on $M$ whose unparametrized geodesics coincide with those of $g$, then $(M,F)$ is a Finsler symmetric space.

math.MG↗