离散循环系统与循环同余
Discrete cyclic systems and circle congruences
摘要：
本文讨论了三维循环系统的可积离散化，即正交坐标系与一族圆坐标线的可积离散化。特别地，详细地研究了基本的圆同余，并通过存在某种平坦联络来刻画。在此框架下，研究了双曲空间中具有一族离散平坦前沿的离散循环系统和所有坐标曲面都是离散Dupin循环的离散循环系统.
英文摘要：
We discuss integrable discretizations of 3-dimensional cyclic systems, that is, orthogonal coordinate systems with one family of circular coordinate lines. In particular, the underlying circle congruences are investigated in detail, and characterized by the existence of a certain flat connection. Within the developed framework, discrete cyclic systems with a family of discrete flat fronts in hyperbolic space and discrete cyclic systems, where all coordinate surfaces are discrete Dupin cyclides, are investigated.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
