论文标题
在3秒的Legendrian曲线的Cauchy-Riemann菌株功能
The Cauchy-Riemann strain functional for Legendrian curves in the 3-sphere
论文作者
论文摘要
研究了三个球体中Legendrian曲线的较低阶段CR不变问题，并推导了其Euler-Lagrange方程。研究了闭合的临界曲线。具有非恒定CR呈壮道的闭合临界曲线是表征的。我们证明他们的Cr-Cr-quer类别与连接的平面域的合理点一对一。描述了一个明确构建所有此类曲线的过程。此外，用三种现象学不变性来对理性参数进行几何解释。
The lower-order cr-invariant variational problem for Legendrian curves in the 3-sphere is studied and its Euler-Lagrange equations are deduced. Closed critical curves are investigated. Closed critical curves with non-constant cr-curvature are characterized. We prove that their cr-equivalence classes are in one-to-one correspondence with the rational points of a connected planar domain. A procedure to explicitly build all such curves is described. In addition, a geometrical interpretation of the rational parameters in terms of three phenomenological invariants is given.
