周期离散达布变换

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2023-10-18 DOI:10.1016/j.difgeo.2023.102065

Joseph Cho , Katrin Leschke , Yuta Ogata

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引用次数: 1

摘要

我们用四元数形式将离散极化曲线的Darboux变换表示为离散连接的平行部分。这立即导致变换的单调性的线性化。我们还考虑了离散自行车对应情形的可积约简。将我们的方法应用于离散圆的情况，我们获得了所有（闭）Darboux变换和（闭）bicycle对应的闭形式离散参数化。

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Periodic discrete Darboux transforms

We express Darboux transformations of discrete polarised curves as parallel sections of discrete connections in the quaternionic formalism. This immediately leads to the linearisation of the monodromy of the transformation. We also consider the integrable reduction to the case of discrete bicycle correspondence. Applying our method to the case of discrete circles, we obtain closed-form discrete parametrisations of all (closed) Darboux transforms and (closed) bicycle correspondences.

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.