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A min-max characterization of Zoll Riemannian metrics

Published online by Cambridge University Press:  29 April 2021

MARCO MAZZUCCHELLI
Affiliation:
Unité de Mathématiques Pures et Appliquées École Normale Supérieure de Lyon, 46 allée d’Italie, 69364 Lyon, France. e-mail: marco.mazzucchelli@ens-lyon.fr
STEFAN SUHR
Affiliation:
Fakultät für Mathematik, Ruhr–Universität Bochum, IB 3/81, Universitätsstr. 150, 44780 Bochum, Germany e-mail: stefan.suhr@rub.de
Corresponding

Abstract

We characterise the Zoll Riemannian metrics on a given simply connected spin closed manifold as those Riemannian metrics for which two suitable min-max values in a finite dimensional loop space coincide. We also show that on odd dimensional Riemannian spheres, when certain pairs of min-max values in the loop space coincide, every point lies on a closed geodesic.

Keywords

Type
Research Article
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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