Morse-Smale characteristic foliations and convexity in contact manifolds

2019/12/03 by Breen, Joseph
#Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1912.01174

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^∞-close to a convex hypersurface.

Related

• C⁰-Contact Geometry of Surfaces in 3-Manifolds
• Convex hypersurface theory in contact topology
• Honda-Huang's work on contact convexity revisited
• Robustly non-convex hypersurfaces in contact manifolds
• Reeb foliations on S⁵ and contact 5-manifolds violating the Thurston-Bennequin inequality