Systolic ratio, index of closed orbits and convexity for tight contact forms on the three-sphere

Autor(es)

Abbondandolo, Alberto ^[1] ; Bramham, Barney ^[1] ; Hryniewicz, Umberto L. ^[2] ; Salomao, Pedro A. S. ^[3]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: COMPOSITIO MATHEMATICA; v. 154, n. 12, p. 2643-2680, DEC 2018.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 16/25053-8 - Dinâmica e geometria em baixas dimensões
• Beneficiário: André Salles de Carvalho
• Modalidade de apoio: Auxílio à Pesquisa - Temático