论文标题
空间形式中恒定散光的旋转表面
Rotational surfaces of constant astigmatism in space forms
论文作者
论文摘要
如果每个点的主曲线主radii之间的差异是恒定函数，则riemannian空间中的表面被称为恒定的散光。在本文中，我们对空间形式中恒定散光的所有旋转表面进行分类。我们还证明，这种表面的生成曲线是曲率能量的差异问题的关键点。使用这些曲线的描述，我们局部构建了恒定散光的所有旋转表面，作为从生成曲线中相关的二维演化表面。
A surface in a Riemannian space is called of constant astigmatism if the difference between the principal radii of curvatures at each point is a constant function. In this paper we give a classification of all rotational surfaces of constant astigmatism in space forms. We also prove that the generating curves of such surfaces are critical points of a variational problem for a curvature energy. Using the description of these curves, we locally construct all rotational surfaces of constant astigmatism as the associated binormal evolution surfaces from the generating curves.
