CR-quadrics with a symmetry property

A characterization of CR quadrics with a symmetry property

We study CR quadrics satisfying a symmetry property $(\tilde S)$ which is slightly weaker than the symmetry property $(S)$, recently introduced by W. Kaup, which requires the existence of an automorphism reversing the gradation of the Lie algebra of infinitesimal automorphisms of the quadric. We characterize quadrics satisfying the $(\tilde S)$ property in terms of their Levi-Tanaka algebras. In many cases the $(\tilde S)$ property implies the $(S)$ property; this holds in particular for compact quadrics. We also give a new example of a quadric such that the dimension of the algebra of positiv…

托勒密-阿尔哈森问题与二次曲面镜反射

The Ptolemy-Alhazen problem and quadric surface mirror reflection

本文探讨球面与二次曲面镜的光反射问题，利用椭圆反射性质推导单位圆焦散曲线，并给出求解二次曲面镜阿尔哈森问题的代数方程。

由垂直对称平面限定的三重周期极小曲面

Triply Periodic Minimal Surfaces Bounded by Vertical Symmetry Planes

基于平面上周期多边形的Schwarz-Christoffel公式，给出了欧几里得空间中许多经典的和新的三重周期极小曲面的统一初等处理.我们的曲面都有一个共同的特性，即垂直对称平面将它们切割成简单连接的片段。