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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

SHARP SYSTOLIC INEQUALITIES FOR RIEMANNIAN AND FINSLER SPHERES OF REVOLUTION

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Author(s):
Abbondandolo, Alberto [1] ; Bramham, Barney [1] ; Hryniewicz, Umberto L. [2] ; Salomao, Pedro A. S. [3]
Total Authors: 4
Affiliation:
[1] Ruhr Univ Bochum, Fac Math, Bochum - Germany
[2] Rhein Westfal TH Aachen, Jakobstr 2, D-52064 Aachen - Germany
[3] Rua Matao 1010, Cidade Univ, BR-05508090 Sao Paulo, SP - Brazil
Total Affiliations: 3
Document type: Journal article
Source: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY; v. 374, n. 3, p. 1815-1845, MAR 2021.
Web of Science Citations: 0
Abstract

We prove that the systolic ratio of a sphere of revolution S does not exceed pi and equals pi if and only if S is Zoll. More generally, we consider the rotationally symmetric Finsler metrics on a sphere of revolution which are defined by shifting the tangent unit circles by a Killing vector field. We prove that in this class of metrics the systolic ratio does not exceed pi and equals pi if and only if the metric is Riemannian and Zoll. (AU)

FAPESP's process: 17/26620-6 - Systolic inequalities for Reeb flows in dimension 3
Grantee:Pedro Antonio Santoro Salomão
Support Opportunities: Scholarships abroad - Research