Séminaires : Séminaire d'Analyse et Géométrie

Equipe(s) :
Responsables :O. Biquard, A. Deruelle, E. Di Nezza, I. Itenberg, X. Ma
Email des responsables : {olivier.biquard, alix.deruelle, eleonora.dinezza, ilia.itenberg, xiaonan.ma}@imj-prg.fr
Salle : 15–25.502
Adresse :Jussieu

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Orateur(s) Marco Mazzucchelli - ENS LYON,
Titre Asymptotically Euclidean metrics without conjugate points are flat
Horaire14:00 à 15:00

In a Riemannian manifold, two points along a geodesic are conjugate when there exists a non-trivial Jacobi field vanishing at those  two points; equivalently, the geodesic ceases to be a locally length-minimizing path past the second point in the conjugate pair. A celebrated theorem of Burago-Ivanov, first established in dimension two by Hopf, asserts that any Riemannian n-torus without conjugate points must be flat. Inspired by this theorem, I will sketch the proof of an analogous result for the Euclidean space: on the n-dimensional Euclidean space, any Riemannian metric that is asymptotic to an order larger than 2 at infinity to the Euclidean metric and has no conjugate points must be isometric to the Euclidean metric.