Self-dual metrics with maximally superintegrable geodesic flows

Abstract

A class of self-dual and geodesically complete spacetimes with maximally superintegrable geodesic flows is constructed by applying the Eisenhart lift to mechanics in pseudo-Euclidean spacetime of signature (1,1). It is characterized by the presence of a second rank Killing tensor. Spacetimes of the ultrahyperbolic signature (2,q) with q > 2, which admit a second rank Killing tensor and possess superintegrable geodesic flows, are built.

V2: 11 pages, minor modifications

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Cited by in corpus (7)

• Superintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separability
• Eisenhart lift for higher derivative systems
• Null lifts and projective dynamics
• Eisenhart lift of Koopman-von Neumann mechanics
• Some metrics admitting nonpolynomial first integrals of the geodesic equation
• More on Jacobi metric: Randers-Finsler metrics, frame dragging and geometrisation techniques
• The Bohlin variant of the Eisenhart lift