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arXiv · 2608.08387

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

Anthony J. García·José Barbosa Gomes·Rafael O. Ruggiero
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Abstract

We study rigidity phenomena in closed Finsler manifolds without conjugate points under assumptions on the $S$-curvature. We prove that a closed $C^\omega$ 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.

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Anthony J. García, José Barbosa Gomes, Rafael O. Ruggiero. 2026-08-09. On rigidity of Finsler manifolds without conjugate points and with constant $S$-curvature. https://arxiv.org/abs/2608.08387

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