双曲平面上非蜕化圆锥截线的聚焦性  

The Focus Properties of Nonsingular Conic Curves in Hyperbolic Plane

作　　者：何海 王幼宁[1] 

机构地区：[1]北京师范大学数学科学学院,北京

出　　处：《理论数学》2017年第4期334-348,共15页Pure Mathematics

基　　金：国家自然科学基金(11171025) (11471039)资助。

摘　　要：众所周知,在平面几何中,从椭圆一个焦点出发的光线被椭圆反射后汇聚于它的另一个焦点;从双曲线的一个焦点出发的光线被双曲线反射后虚汇聚于它的另一个焦点;而对于抛物线来说,从焦点出发的光线被抛物线反射成为平行光。本文证明了双曲平面上的非蜕化圆锥截线也有相应的聚焦性;而且,存在一些非圆锥截线的曲线,它们也有聚焦性。In the plane geometry, as we all know, the light through a focus of the ellipse is reflected by ellipse to focus on another;similarly the light through the hyperbola one focus, after reflection, reversely focuses on another;and for the parabola it is true that the light from focus is reflected into parallel light. This paper proved that the nonsingular conic curves on the hyperbolic plane have corresponding focus properties;moreover, there are some curves having focusing properties, which are not conic curves.

关 键 词：双曲平面 圆锥截线 聚焦性 Beltrami-Klein坐标系 

分 类 号：G6[文化科学—教育学]