Great circle fibrations and contact structures on the 3-sphere

被引：0
|
作者：
Herman Gluck
机构：
[1] Herman Gluck,Department of Mathematics
[2] University of Pennsylvania,undefined
来源：
Geometriae Dedicata | 2022年 / 216卷
关键词：
Hopf fibration of the 3-sphere; Tight contact structure; Fibrations of spheres by great circles;
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摘要：
Given any smooth fibration of the unit 3-sphere by great circles, we show that the distribution of 2-planes orthogonal to the great circle fibres is a tight contact structure, a fact well known in the special case of the Hopf fibrations. The proof expresses hypothesis and conclusion as differential inequalities involving functions on disks transverse to the fibres, and shows that one inequality implies the other.
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