Constrained elastic curves and surfaces with spherical curvature lines
Constrained elastic curves and surfaces with spherical curvature lines
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具有球面曲率线的约束弹性曲线和曲面
DOI：
10.1512/iumj.2023.72.9487
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发表时间：
2021
影响因子：
1.1
通讯作者：
Gudrun Szewieczek
中科院分区：
文献类型：
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作者：
Joseph Cho;M. Pember;Gudrun Szewieczek
本文考虑具有一族或两族球面曲率线的曲面。我们表明，每一个表面的一个家庭的球面曲率线可以本地生成的一对初始数据：一个合适的曲线的李球变换和球面勒让德曲线。然后，我们提供的条件，这样的表面是李适用的初始数据，一类可积的表面，包括CMC和伪球面。特别地，我们证明了具有恰好一族球面曲率线的Lie适用曲面必须由某种空间形式中的约束弹性曲线的提升生成。基于这一目标，我们利用一类联络的多项式守恒量给出了约束弹性曲线的Lie球几何刻画。
In this paper we consider surfaces with one or two families of spherical curvature lines. We show that every surface with a family of spherical curvature lines can locally be generated by a pair of initial data: a suitable curve of Lie sphere transformations and a spherical Legendre curve. We then provide conditions on the initial data for which such a surface is Lie applicable, an integrable class of surfaces that includes cmc and pseudospherical surfaces. In particular we show that a Lie applicable surface with exactly one family of spherical curvature lines must be generated by the lift of a constrained elastic curve in some space form. In view of this goal, we give a Lie sphere geometric characterisation of constrained elastic curves via polynomial conserved quantities of a certain family of connections.
影响因子：
0.6
作者：
Cho Joseph;Leschke Katrin;Ogata Yuta;Ogata Yuta
通讯作者：
Ogata Yuta