Symmetry classification of viscid flows on space curves

Differential invariants for flows of fluids and gases

This paper surveys results found by the authors in the previous papers (see for example, A. Duyunova, V. Lychagin, S. Tychkov, Differential invariants for spherical layer flows of a viscid fluid, Journal of Geometry and Physics, 130, 288-292 (2018)) concerning calculation and classification of symmetry Lie algebra and differential invariants for a variety of fundamental systems in fluid mechanics, including the Euler and Navier-Stokes equations on a plane, three-dimensional space, a sphere, and a spherical layer. In each case, the symmetry Lie algebra is found, followed by a list of generating…

Galilean Classification of Curves

In this paper, we classify space-time curves up to Galilean group of transformations with Cartan's method of equivalence. As an aim, we elicit invariats from action of special Galilean group on space-time curves, that are, in fact, conservation laws in physics. We also state a necessary and sufficient condition for equivalent Galilean motions.

H^3 中 Killing 磁曲线的分类

Classification of Killing Magnetic Curves In H^3

本文解析求解 H^3 的测地线方程，利用一阶微扰法计算六个 Killing 向量场生成的磁曲线轨迹并与数值解对比，同时证明 3 维 (α)-Kenmotsu 流形不存在沿 Reeb 向量场方向的磁场向量场。

(非)受挫二维伊辛模型在亏格为1的等径图上的分类

Classification of (non)-frustrated 2D Ising models in genus 1 on isoradial graphs

本文对亏格为1的等径图上受挫和非受挫二维伊辛模型进行了完整分类，并扩展了Baxter模型至实耦合常数。