| Full text | |
| 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, Fak Math, Univ Str 150, D-44801 Bochum - Germany
[2] Univ Fed Rio de Janeiro, Dept Matemat Aplicada, Av Athos da Silveira Ramos 149, BR-21941909 Rio De Janeiro, RJ - Brazil
[3] Univ Sao Paulo, Inst Matemat & Estat, Dept Matemat, Rua Matao, 1010 Cidade Univ, BR-05508090 Sao Paulo, SP - Brazil
Total Affiliations: 3
|
| Document type: | Journal article |
| Source: | COMPOSITIO MATHEMATICA; v. 154, n. 12, p. 2643-2680, DEC 2018. |
| Web of Science Citations: | 0 |
| Abstract | |
We construct a dynamically convex contact form on the three-sphere whose systolic ratio is arbitrarily close to 2. This example is related to a conjecture of Viterbo, whose validity would imply that the systolic ratio of a convex contact form does not exceed 1. We also construct, for every integer n >= 2, a tight contact form with systolic ratio arbitrarily close to n and with suitable bounds on the mean rotation number of all the closed orbits of the induced Reeb flow. (AU) | |
| FAPESP's process: | 16/25053-8 - Dynamics and geometry in low dimensions |
| Grantee: | André Salles de Carvalho |
| Support Opportunities: | Research Projects - Thematic Grants |