Discrete Invariant Curve Flows, Orthogonal Polynomials, and Moving Frame
Discrete Invariant Curve Flows, Orthogonal Polynomials, and Moving Frame
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离散不变曲线流、正交多项式和移动框架
DOI：
10.1093/imrn/rnz379
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发表时间：
--
影响因子：
1
通讯作者：
Li Shi-Hao
中科院分区：
文献类型：
--
作者：
Wang Bao;Chang Xiang-Ke;Hu Xing-Biao;Li Shi-Hao
提出了一种基于正交多项式(OPS)的离散运动帧和不变量生成方法。结果表明，OPS可以给出离散运动标架及其相关的差分不变量的显式表达式，该方法使人们能够同时获得相应的离散不变曲线流。给出了中心仿射平面、伪欧氏平面和高维中心仿射空间的几个例子。
In this paper, an orthogonal polynomials-based (OPs-based) approach to generate discrete moving frames and invariants is developed. It is shown that OPs can provide explicit expressions for the discrete moving frame as well as the associated difference invariants, and this approach enables one to obtain the corresponding discrete invariant curve flows simultaneously. Several examples in the cases of centro-affine plane, pseudo-Euclidean plane, and high-dimensional centro-affine space are presented.