Tightness in contact metric 3-manifolds

Details Tightness in contact metric 3-manifolds Tightness in contact metric 3-manifolds

2009-06-18

arxiv.org/abs/0906.3487v3

Mathematics

Symplectic Geometry

29 pages. Added the sphere theorem, removed high dimensional material and an alternate approach to the three dimensional tight

Scientific paper

This paper begins the study of relations between Riemannian geometry and global properties of contact structures on 3-manifolds. In particular we prove an analog of the sphere theorem from Riemannian geometry in the setting of contact geometry. Specifically, if a given three dimensional contact manifold (M,\xi) admits a complete compatible Riemannian metric of positive 4/9-pinched curvature then the underlying contact structure \xi is tight; in particular, the contact structure pulled back to the universal cover is the standard contact structure on S^3. We also describe geometric conditions in dimension three for \xi to be universally tight in the nonpositive curvature setting.

Affiliated with

Also associated with

No associations

Rating

Tightness in contact metric 3-manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Tightness in contact metric 3-manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Tightness in contact metric 3-manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-725859