曲线在直纹表面上的微小弯曲

Marija S. Najdanovic, L. Velimirović
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引用次数: 4

摘要

本文研究了欧几里德三维空间中直纹曲面上曲线的无穷小弯曲问题。我们得到了一个无穷小弯曲场,在其作用下,所有弯曲曲线都保持在与初始曲线相同的直纹表面上。特别地,我们考虑了圆柱曲线和双曲抛物面曲线的无穷小弯曲,并找到了相应的无穷小弯曲场。研究了双曲抛物面无穷小弯曲下曲线曲率的变化。用Mathematica程序包对一些例子进行了可视化。
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Infinitesimal bending of curves on the ruled surfaces
In this paper we study infinitesimal bending of curves that lie on the ruled surfaces in Euclidean 3-dimensional space. We obtain an infinitesimal bending field under whose effect all bent curves remain on the same ruled surface as the initial curve. Specially, we consider infinitesimal bending of the curves which belong to the cylinder as well as to the hyperbolic paraboloid and find corresponding infinitesimal bending fields. We examine the variation of the curvature of a curve under infinitesimal bending on the hyperbolic paraboloid. Some examples are visualized using program packet Mathematica.
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