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SUMMARY:Andreas Vollmer (Politecnico di Torino)
DTSTART:20201120T155000Z
DTEND:20201120T163000Z
DTSTAMP:20260423T021222Z
UID:DGSTO/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/DGSTO/5/">Tw
 o-dimensional superintegrable metrics with symmetries that preserve geodes
 ic curves</a>\nby Andreas Vollmer (Politecnico di Torino) as part of Diffe
 rential Geometry Seminar Torino\n\n\nAbstract\nIn 1882\, Sophus Lie formul
 ated the task to describe two-dimensional metrics admitting non-trivial sy
 mmetries that preserve geodesics up to reparametrisation. Such symmetries 
 are called projective. Lie's Problem has been resolved in recent years in 
 terms of a classification up to diffeomorphisms (Bryant-Manno-Matveev 2008
 \, Matveev 2012 and Manno-V 2020).\n\nThe talk will focus on a distinct su
 bclass of these metrics\, namely those that are superintegrable with quadr
 atic integrals of motion. Generally speaking a metric is superintegrable i
 f it admits a maximal amount of independent constants of motion.\nMatveev'
 s geometries are a particular example\, in which case the projective symme
 try is unique. It turns out that all of Matveev's geometries share the sam
 e geodesics up to reparametrisation (in other words\, they are projectivel
 y equivalent). The associated superintegrable systems are of non-degenerat
 e type meaning that they admit a four-parameter potential.\n\nThis talk wi
 ll be held on the occasion of the PRIN seminar organised by the Politecnic
 o di Torino PRIN unit.\n
LOCATION:https://researchseminars.org/talk/DGSTO/5/
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