论文标题
海森伯格集团中的legendrian叶子和二次差异的模量
Moduli of Legendrian foliations and quadratic differentials in the Heisenberg group
论文作者
论文摘要
本文的目的是证明海森堡集团曲线家族模量的以下结果。让$ω$为由家庭$γ$ legendrian曲线育成的海森伯格集团的一个领域。假设在\ cite {tim2}中定义的操作员的内核上有二次差异$ q $，并且$γ$中的每条曲线都是$ q $的水平轨迹。令$l_γ：ω\ rightArrow] 0，+\ infty [$是将$ p \ inω$的点$ p \ inω$，$ q $ - lengength incopt $ p $的函数。然后，$γ$的模量为\ [m_4（γ）= \int_Ω\ frac {| q |^2} {（l_γ）^4} \ mathrm {d} l^3。\]
The aim of the paper is to prove the following result concerning moduli of curve families in the Heisenberg group. Let $Ω$ be a domain in the Heisenberg group foliated by a family $Γ$ of legendrian curves. Assume that there is a quadratic differential $q$ on $Ω$ in the kernel of an operator defined in \cite{Tim2} and every curve in $Γ$ is a horizontal trajectory for $q$. Let $l_Γ: Ω\rightarrow ]0,+\infty[$ be the function that associates to a point $p\in Ω$, the $q$-length of the leaf containing $p$. Then, the modulus of $Γ$ is \[ M_4 (Γ) = \int_Ω\frac{|q|^2}{(l_Γ) ^4} \mathrm{d} L^3.\]
