Zoll and Tannery metrics from a superintegrable geodesic flow

Abstract

We prove that for Matveev and Shevchishin superintegrable system, with a linear and a cubic integral, the metrics defined on S^2 and on Tannery's orbifold T^2 are either Zoll or Tannery metrics.

arXiv comment13 pages, no figure

References in corpus (2)

• Superintegrable Systems in Darboux spaces
• Two-dimensional superintegrable metrics with one linear and one cubic integral

Cited by in corpus (2)

• Explicit metrics for a class of two-dimensional superintegrable systems
• Global structure and geodesics for Koenigs superintegrable systems