Analysis of Timelike Thomsen Surfaces
Analysis of Timelike Thomsen Surfaces
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DOI：
10.1007/s12220-019-00166-7
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发表时间：
2018-08
期刊：
影响因子：
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通讯作者：
S. Akamine;Joseph Cho;Yuta Ogata
中科院分区：
文献类型：
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作者：
S. Akamine;Joseph Cho;Yuta Ogata
类时极小曲面是类时极小曲面，也是仿射极小曲面。在本文中，我们利用洛伦兹共形坐标和零坐标，以及它们各自的表现定理的类时极小曲面，得到一个完整的整体分类，这些表面和他们使用的几何不变量称为类光曲率的特征。结果，我们揭示了类时曲面和具有平面曲率线的类时极小曲面之间的关系。作为应用，给出了保伪弧长参数化和类光曲率不变的零曲线变形。
Timelike Thomsen surfaces are timelike minimal surfaces that are also affine minimal. In this paper, we make use of both the Lorentz conformal coordinates and the null coordinates, and their respective representation theorems of timelike minimal surfaces, to obtain a complete global classification of these surfaces and to characterize them using a geometric invariant called lightlike curvatures. As a result, we reveal the relationship between timelike Thomsen surfaces, and timelike minimal surfaces with planar curvature lines. As an application, we give a deformation of null curves preserving the pseudo-arclength parametrization and the constancy of the lightlike curvatures.