Integrable geodesic flow in 3D and webs of maximal rank

2024/03/03 by Sergey I. Agafonov, Agafonov, Sergey I.
Computer Science · Mathematics · #37J06 #53A60 #Computer Graphics and Visualization Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2403.01459

openalex publication_date 2024/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize geodesic flows, admitting two commuting quadratic integrals with common principal directions, in terms of the geodesic 4-webs such that the tangents to the web leaves are common zero directions of the integrals. We prove that, under some natural geometric hypothesis, the metric is of Stäckel type.

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