2018/02/11 by Herman Gluck, Gluck, Herman
Engineering · Mathematics · #Elasticity and Material Modeling #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #math.AT #math.DG #math.GT #math.SG
paper · pdf · doi:10.48550/arxiv.1802.03797
19 pages, 5 figures, Differential Geometry, Contact Geometry, Manifolds and Cell Complexes
arxiv created 2018/02/11 · arxiv updated 2018/02/13
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.