ON THE EXISTENCE OF DISK-LIKE GLOBAL SECTIONS FOR REEB FLOWS ON THE TIGHT 3-SPHERE

被引：27

作者：

Hryniewicz, Umberto ^{[1
]}

Salomao, Pedro A. S. ^{[2
]}

机构：

[1] Univ Fed Rio de Janeiro, Dept Matemat Aplicada, Inst Matemat, Rio De Janeiro, Brazil

[2] Univ Sao Paulo, Dept Matemat, Inst Matemat & Estat, BR-05508 Sao Paulo, Brazil

来源：

DUKE MATHEMATICAL JOURNAL | 2011年 / 160卷 / 03期

基金：

巴西圣保罗研究基金会;

关键词：

PSEUDO-HOLOMORPHIC-CURVES; PSEUDOHOLOMORPHIC CURVES; SYMPLECTISATIONS;

D O I：

10.1215/00127094-1444278

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider Reeb dynamics on the 3-sphere associated to a tight contact form. Our main result gives necessary and sufficient conditions for a periodic Reeb orbit to bound a disk-like global section for the Reeb flow, when the contact form is assumed to be nondegenerate.

引用

页码：415 / 465

页数：51

共 24 条

[1]

Bennequin Daniel, 1983, Asterisque, V107, P87

[2] Compactness results in Symplectic Field Theory [J].

Bourgeois, F ;

Eliashberg, Y ;

Hofer, H ;

Wysocki, K ;

Zehnder, E .

GEOMETRY & TOPOLOGY, 2003, 7 :799-888

[3]

Cieliebak K, 2005, J SYMPLECT GEOM, V3, P589

[4] CONTACT 3-MANIFOLDS 20 YEARS SINCE MARTINET,J. WORK [J].

ELIASHBERG, Y .

ANNALES DE L INSTITUT FOURIER, 1992, 42 (1-2) :165-192

[5]

Eliashberg Y, 2000, GEOM FUNCT ANAL, P560

[6]

Eliashberg Y., 1990, Geometry of Low-Dimensional Manifolds: Symplectic Manifolds and Jones-Witten Theory, V2, P45, DOI DOI 10.1017/CBO9780511629341.006

[7] GEODESICS ON S-2 AND PERIODIC POINTS OF ANNULUS HOMEOMORPHISMS [J].

FRANKS, J .

INVENTIONES MATHEMATICAE, 1992, 108 (02) :403-418

[8] PSEUDO HOLOMORPHIC-CURVES IN SYMPLECTIC-MANIFOLDS [J].

GROMOV, M .

INVENTIONES MATHEMATICAE, 1985, 82 (02) :307-347

[9]

HBYNIEWICZ U., T AM MATH S IN PRESS

[10] The dynamics on three-dimensional strictly convex energy surfaces [J].

Hofer, H ;

Wysocki, K ;

Zehnder, E .

ANNALS OF MATHEMATICS, 1998, 148 (01) :197-289

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