1/4-Pinched Contact Sphere Theorem
Differential Geometry
2013-04-19 v1 Geometric Topology
Symplectic Geometry
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.
Cite
@article{arxiv.1304.5224,
title = {1/4-Pinched Contact Sphere Theorem},
author = {Jian Ge and Yang Huang},
journal= {arXiv preprint arXiv:1304.5224},
year = {2013}
}