Morse-Smale characteristic foliations and convexity in contact manifolds

Abstract

We generalize a result of Giroux which says that a closed surface in a contact $3$-manifold with Morse-Smale characteristic foliation is convex. Specifically, we show that the result holds in contact manifolds of arbitrary dimension. As an application, we show that a particular closed hypersurface introduced by A. Mori is $C^{\infty }$-close to a convex hypersurface.

11 pages, 3 figures. v2: minor typos, added references and corrected a theorem attribution