主二重线的多维一致性
Multi-dimensional consistency of principal binets
AI总结：
本文提出主二重线作为离散曲面参数化方法，证明其在多维一致性下的可积性，并推广到更高维晶格，同时探讨其与离散正交坐标系统的关系。
摘要：
主二重线是一种定义在正方形晶格Z²顶点和面上的曲率线参数化表面的离散化。它们推广了之前由圆网、锥形网和主接触元素网所确立的离散化方法。我们证明主二重线在多维一致性意义上构成一个离散可积系统。特别是，它们可以推广到更高维度的正方形晶格Z^N。我们还讨论了它们与之前为离散共焦点四面体所确立的离散正交坐标系统的关系。
英文摘要：
Principal binets are a discretization of curvature line parametrized surfaces defined on the vertices and faces of the square lattice $\Z^2$. They generalize the previously established discretizations given by circular nets, conical nets, and principal contact element nets. We show that principal binets constitute a discrete integrable system in the sense of multi-dimensional consistency. In particular, they generalize to higher-dimensional square lattices $\Z^N$. We also discuss relations to the notion of discrete orthogonal coordinate systems as previously established for discrete confocal quadrics.
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。
