论文标题
在三个球体中的横向曲线的Cauchy-Riemann几何形状上
On the Cauchy-Riemann geometry of transversal curves in the 3-sphere
论文作者
论文摘要
令$ \ mathrm s^3 $为$ \ mathbb c^2 $的单位领域，其标准cauchy-riemann（CR）结构。本文使用$ \ mathrm s^3 $的本地CR不变式调查了$ \ Mathrm S^3 $中曲线的CR几何形状。更具体地说，重点是横向结的CR几何形状。考虑了四个全球横向结的全局不变剂：相异常，CR旋转，Maslov索引和CR自链数。讨论了这些不变的人与打结的本纳金数之间的相互作用。接下来，考虑了通用横向曲线的最简单CR不变性问题，并研究了其闭合的临界曲线。
Let $\mathrm S^3$ be the unit sphere of $\mathbb C^2$ with its standard Cauchy-Riemann (CR) structure. This paper investigates the CR geometry of curves in $\mathrm S^3$ which are transversal to the contact distribution, using the local CR invariants of $\mathrm S^3$. More specifically, the focus is on the CR geometry of transversal knots. Four global invariants of transversal knots are considered: the phase anomaly, the CR spin, the Maslov index, and the CR self-linking number. The interplay between these invariants and the Bennequin number of a knot are discussed. Next, the simplest CR invariant variational problem for generic transversal curves is considered and its closed critical curves are studied.
