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

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)


53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)


Zbl 0742.53010
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