论文标题
统一组上的莫比乌斯流体动力学] {单一组上的möbius流体动力学
Mobius fluid dynamics on the unitary groups]{Möbius fluid dynamics on the unitary groups
论文作者
论文摘要
我们研究了分裂统一组的标准异性动作$ g = o_ {o_ {o} \ left（n，n \ right）$，$ su \ left（n，n，n \ right）$和$ sp \ left（n，n，n，n \ right）$在紧凑型经典lie组上， 分别。更确切地说，我们研究了与$ g $在$ m上的动作相关的$％g $的几何形状，假设$ m $ $ $ $ $ $ M $具有其规范的双势riemannian量表，并且最初是质量分布的。至少动作原则，无力动作（$ g $中的曲线）对应于$ g $的大地测量。地球方程可以理解为具有Möbius约束的无粘性汉堡方程。我们证明，$ g $的动能指标尚未完成，尤其不是不变的，找到$ g $的对称性和完全的地球次级submanifolds，并解决了以下问题。此外，我们研究了在低维度中与球体的保形和投射运动动力学的等效性。
We study the nonrigid dynamics induced by the standard birational actions of the split unitary groups $G=O_{o}\left( n,n\right) $, $SU\left( n,n\right) $ and $Sp\left( n,n\right) $ on the compact classical Lie groups $M=SO_{n}$, $% U_{n}$ and $Sp_{n}$, respectively. More precisely, we study the geometry of $% G$ endowed with the kinetic energy metric associated with the action of $G$ on $M,$ assuming that $M$ carries its canonical bi-invariant Riemannian metric and has initially a homogeneous distribution of mass. By the least action principle, force free motions (thought of as curves in $G$) correspond to geodesics of $G$. The geodesic equation may be understood as an inviscid Burgers equation with Möbius constraints. We prove that the kinetic energy metric on $G$ is not complete and in particular not invariant, find symmetries and totally geodesic submanifolds of $G$ and address the question under which conditions geodesics of rigid motions are geodesics of $G$. Besides, we study equivalences with the dynamics of conformal and projective motions of the sphere in low dimensions.
