Great circle fibrations and contact structures on the 3-sphere

Gluck Herman

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Great circle fibrations and contact structures on the 3-sphere

机译：3 球体上的大圆纤维和接触结构

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Abstract 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.

机译：摘要给定单元3球体被大圆平滑纤维化，表明与大圆纤维正交的2平面分布是紧密接触结构，这一事实在Hopf纤维的特殊情况下是众所周知的。该证明将假设和结论表示为涉及横于纤维的圆盘上的函数的微分不等式，并表明一个不等式意味着另一个不等式。

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来源
《Geometriae Dedicata》 |2022年第6期|共5页
作者
Gluck Herman;
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作者单位

Herman Gluck, University of Pennsylvania;

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原文格式 PDF
正文语种英语
中图分类几何、拓扑;
关键词
Hopf fibration of the 3-sphere; Tight contact structure; Fibrations of spheres by great circles;

机译：3 球体的 Hopf 纤维化;紧密接触结构;大圆球体的纤维化;

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机译：The Arc Complex and Contact Geometry: Nondestabilizable Planar Open Book Decompositions of the Tight Contact 3-Sphere
3. Tight contact structures on Seifert manifolds over T2 with one singular fibre [J] . Ghiggini Paolo Algebraic & geometric topology . 2005,第2期

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Great circle fibrations and contact structures on the 3-sphere

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