We prove (under some technical assumptions) that each surface in ${\mathbb{R}}^3$ containing two arcs of parabolas with axes parallel to Oz through each point has a parametrization $(\frac{P(u,v)}{R(u,v)},\frac{Q(u,v)}{R(u,v)},\frac{Z(u,v)}{R^2(u,v)})$ for some $P,Q,R,Z\in \mathbb{R}[u,v]$ such that $P,Q,R$ have degree at most 1 in u and v, and Z has degree at most 2 in u and v. The proof is based on the observation that one can consider a parabola with vertical axis as an isotropic circle; this allows us to use methods of the recent work by M. Skopenkov and R. Krasauskas in which all surfaces containing two Euclidean circles through each point are classified. Such approach also allows us to find a similar parametrization for surfaces in ${\mathbb{R}}^3$ containing two arbitrary isotropic circles through each point (under the same technical assumptions). Finally, we get some results concerning the top view (the projection along the Oz axis) of the surfaces in question.

我们证明（在一些技术假设下）每个表面 ${\mathbb{电阻}}^3$包含两条轴平行于Oz通过每个点的抛物线弧具有参数化$(\frac{磷(你,v)}{\mathrm{电阻}(你,v)},\frac{问(你,v)}{\mathrm{电阻}(你,v)},\frac{Z(你,v)}{{\mathrm{电阻}}^2(你,v)})$ 对于一些 $磷,问,\mathrm{电阻},Z\in \mathbb{电阻}[你,v]$ 以至于 $磷,问,\mathrm{电阻}$在最多1度ü和v，以及ž至多2度ü和v。证明是基于以下观察：可以将纵轴的抛物线视为各向同性圆；这使我们能够使用 M. Skopenkov 和 R. Krasauskas 最近工作的方法，其中对通过每个点包含两个欧几里得圆的所有表面进行分类。这种方法还允许我们找到类似的曲面参数化${\mathbb{电阻}}^3$包含通过每个点的两个任意各向同性圆（在相同的技术假设下）。最后，我们得到了有关表面的顶视图（沿Oz轴的投影）的一些结果。