Asian Journal of Mathematics
Volume 20 (2016)
$1/4$-pinched contact sphere theorem
Pages: 893 – 902
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.
contact sphere theorem, curvature, tight contact structure
2010 Mathematics Subject Classification
Primary 53D10. Secondary 53B20.