Differential invariants for cubic integrals of geodesic flows on surfaces

Abstract

We construct differential invariants that vanish if and only if the geodesic flow of a 2-dimensional metric admits an integral of 3rd degree in momenta with a given Birkhoff-Kolokoltsov 3-codifferential.

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References in corpus (5)

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Cited by in corpus (6)

• Two-dimensional superintegrable metrics with one linear and one cubic integral
• On natural Poisson bivectors on the sphere
• Hydrodynamic-type systems describing 2-dimensional polynomially integrable geodesic flows
• When a $(1,1)$-tensor generates separation of variables of a certain metric
• The geometry of a positively curved Zoll surface of revolution
• Real-analyticity of 2-dimensional superintegrable metrics and solution of two Bolsinov-Kozlov-Fomenko conjectures