双曲空间型中圆锥截线的度量几何分类

Metrical Geometry Classification of Conic Section in Hyperbolic Space Form

本文定义了双曲平面中的抛物线的一个度量不变量系统。在Beltrami-Klein坐标系下讨论了抛物线的方程和直观,并引入极限椭圆和极限双曲线作为抛物线的极限情形。给出了双曲空间中的圆锥截线的分类,该分类不同于欧氏空间中的相应情形。

The paper defines a metric invariant system of parabola in hyperbolic plane. The equation and the figures of parabola are discussed in Beltrami-Klein coordinates. Limit ellipse and limit hyperbola are limiting case of parabola in this way. The classification of conic section in hyperbolic space will be given, which is different with that immersed in Euclid space.