Convexité en topologie de contact. (Convexity in contact topology). (French) Zbl 0766.53028

Giroux, Emmanuel

Comment. Math. Helv. 66, No. 4, 637-677 (1991).

A contact structure \(\xi\) on a manifold \(V\) is convex if there exists a proper Morse function \(f: V\to[0,\infty)\) with a gradient-like vector field preserving \(\xi\) [Ya. Eliashberg and M. Gromov, Convex symplectic manifolds, Several complex variables and complex geometry, Proc. Summer Res. Inst., Santa Cruz/Ca (USA) 1989, Proc. Symp. Pure Math. 52, Part 2, 135-162 (1991; Zbl 0742.53010)]. The author studies the characteristic foliations on a surface \(S\) in a 3-dimensional contact manifold and presents a construction of convex contact structures in dimension 3.

Reviewer: V.Oproiu (Iaşi)

MSC:

53C15

General geometric structures on manifolds (almost complex, almost product structures, etc.)

Keywords:

Morse function; characteristic foliations; convex contact structures

Citations:

Zbl 0742.53010