论文标题
与坐标有限型高斯图中的不变表面，在各向同性空间中
Invariant surfaces with coordinate finite-type Gauss map in simply isotropic space
论文作者
论文摘要
我们考虑了简单的各向同性空间中表面的外部几何形状，这是一个三维空间，配备了索引零等级2度量。由于公制是退化的，因此不能仅根据度量特性明确定义表面法线。为了理解各向同性高斯图的不同选择之间的对比，在这里，我们使用高斯图研究表面，其坐标是表面拉普拉斯 - 贝特拉米操作员的特征函数。我们考虑了两种选择，即所谓的最小和抛物线属官方，并表明，当应用于简单的不变性表面时，相应的高斯映射的坐标是征征函数会导致平面，某些圆柱体或具有常数同位素平均平均曲率的表面。最后，我们还使用谐波高斯图调查（非不必要的）表面，并表明这表征了恒定的平均曲率表面。
We consider the extrinsic geometry of surfaces in simply isotropic space, a three-dimensional space equipped with a rank 2 metric of index zero. Since the metric is degenerate, a surface normal cannot be unequivocally defined based on metric properties only. To understand the contrast between distinct choices of an isotropic Gauss map, here we study surfaces with a Gauss map whose coordinates are eigenfunctions of the surface Laplace-Beltrami operator. We take into account two choices, the so-called minimal and parabolic normals, and show that when applied to simply isotropic invariant surfaces the condition that the coordinates of the corresponding Gauss map are eigenfunctions leads to planes, certain cylinders, or surfaces with constant isotropic mean curvature. Finally, we also investigate (non-necessarily invariant) surfaces with harmonic Gauss map and show this characterizes constant mean curvature surfaces.
