关于Lorenzoni-Magri流体动力学型层次结构
数学物理
2024-09-04 v3 微分几何
math.MP
可精确求解与可积系统
摘要
2005年，Lorenzoni和Magri证明了由具有消失Nijenhuis挠率的(1,1)型张量场的幂次所确定的流体动力学型层次结构，可以借助新层次守恒律链变形为更一般的层次结构。我们回顾了这一构造。所得层次的(1,1)型张量场通常具有非零的Nijenhuis挠率，但其Haantjes张量为零。
引用
@article{arxiv.2404.10562,
title = {On the Lorenzoni-Magri hierarchy of hydrodynamic type},
author = {Folkert Müller-Hoissen},
journal= {arXiv preprint arXiv:2404.10562},
year = {2024}
}
备注
12 pages, third version: Proposition 3.1 in previous versions was incorrect and has been deleted, Theorem 4.5 follows directly from a result of Bogoyavlenskij in 2004, corresponding note added at the end of the paper