1/4-Pinched Contact Sphere Theorem

2013/04/18 by Jian Ge, Yang Huang, Ge, Jian +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG) #math.DG #math.GT #math.SG

paper · pdf · doi:10.48550/arxiv.1304.5224

arxiv created 2013/04/18 · arxiv updated 2013/04/19

Abstract

Given a closed contact 3-manifold with a compatible Riemannian metric, we show that if the sectional curvature is 1/4-pinched, then the contact structure is universally tight. This result improves the Contact Sphere Theorem in [EKM12], where a 4/9-pinching constant was imposed. Some tightness results on positively curved contact open 3-manifold are also discussed.

Related

• Tightness in contact metric 3-manifolds
• The space of tight contact structures on \mathbb R³ is contractible
• A sphere theorem for three dimensional manifolds with integral pinched curvature
• Quantitative tightness for three-dimensional contact manifolds: a sub-Riemannian approach
• A cut-and-paste approach to contact topology