Vortex Filaments in Hermitian Reductive Lie Algebras
arXiv:2607.26650
The paper extends the geometric theory of vortex filament dynamics from Euclidean space and Hermitian symmetric Lie algebras to the broader setting of Hermitian reductive Lie algebras, deriving three vortex models that reduce to the known ones when the algebra collapses to a symmetric case.
Abstract
It is well-known that the investigation of vortex filaments (i.e., moving curves) in the Euclidean 3-space 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 equi-collapses to a Hermitian symmetric Lie algebra , they revert respectively to those in .
36 pages. Comments are welcome