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SUMMARY:Conformal aspects of submanifolds and curves - Rod Gover (Universi
 ty of Auckland)
DTSTART:20240903T133000Z
DTEND:20240903T143000Z
UID:TALK219862@talks.cam.ac.uk
DESCRIPTION:We develop a comprehensive tractor based theory and calculus f
 or conformal submanifolds.This includes a conformally invariant Gauss-Coda
 zzi-Ricci theory\, and canbe used for example to proliferate submanifold i
 nvariants. The set-up is designed tooptimally capture links to the conform
 al sphere as model and within that a correspondencespace picture of the di
 stinguished totally geodesic submanifolds.On general conformal manifolds w
 e show that the equations for unparametrisedconformal geodesics are the sp
 ecial case of a uniform notion of distinguished submanifolds.Moreover this
  class of special submanifolds is exactly the class that is weaklyconforma
 lly geodesic\, meaning that ambient conformal geodesics remain in the subm
 anifold.For conformal geodesics and and such distinguished submanifolds th
 ere isan essentially uniform way to construct first integrals from suitabl
 e solutions of firstBGG equations.Moreover the notions of minimal submanif
 olds\, CMC submanifolds\, and relatedconcepts are also nicely captured in 
 the tractor theory for submanifolds that we develop\,and this also means t
 hese notions are generalised in that they are well defined atthe conformal
  singularities of metrics\, as arise in Poincare-Einstein (and more genera
 llyconformally compact metrics). This applies in particular to geodesics w
 hich maybe viewed as minimal 1-manifolds. This description of minimal subm
 anifolds also providessimpler proofs of some recent results in the literat
 ure\, and this will be described.This is joint work with Sean Curry and Da
 niel Snell.
LOCATION:Seminar Room 2\, Newton Institute
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