AI 中文总结
本文以纯几何方式将涡旋丝理论推广至埃尔米特约化李代数，所得涡旋模型在等坍缩为埃尔米特对称李代数时可对应退化，丰富了相关几何与物理研究内容。
AI 中文摘要
众所周知，对欧几里得3维空间$\boldsymbol{\text{R}}^3$中涡旋丝（即运动曲线）的研究是物理学和数学中一个颇具吸引力的课题，该理论主要包含到三阶近似为止的三种涡旋模型。这一理论在数学中已成功推广到具有物理和几何背景的埃尔米特对称李代数。本文致力于以纯几何的方式将其发展到埃尔米特约化李代数，所得到的三种涡旋模型满足：当埃尔米特约化李代数$\boldsymbol{\frak g}$等坍缩为埃尔米特对称李代数$\boldsymbol{\frak h}$时，它们分别退化为$\boldsymbol{\frak h}$中的对应模型。
英文摘要
It is well-known that the investigation of vortex filaments (i.e., moving curves) in the Euclidean 3-space $\mathbb R^3$ is an attractive topic both in physics and mathematics. The theory consists mainly of the three vortex models, up to the third-order approximation. Such a theory has been successfully extended to Hermitian symmetric Lie algebras in mathematics with physical and geometrical backgrounds. This article is devoted to developing it to Hermitian reductive Lie algebras in a purely geometric way. The three vortex models obtained in this article fulfill that when the Hermitian reductive Lie algebra ${\mathfrak g}$ equi-collapses to a Hermitian symmetric Lie algebra ${\mathfrak h}$, they revert respectively to those in ${\mathfrak h}$.
Comments36 pages. Comments are welcome
