Convexité en topologie de contact. (Convexity in contact topology) (Q1190213)

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 \(\xi\) [\textit{Ya. Eliashberg} and \textit{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.