二次曲面的保型性探讨

On Simplification of Type-Preserving Problems of Quadratic Surfaces

本文通过研究过定点的二次曲面动弦中点的轨迹方程∑′和定点与二次曲面上动点之间定比分点的轨迹方程∑,″将十七种二次曲面的衍生轨迹∑′和∑″的保型性问题进行讨论,并得到关于二次曲面保型性的两个重要结论.

This paper addresses the orbit equation ∑′ passing a fixed point and the midpoint in the secant of a fixed quadratic surface and the orbit equation ∑″ of a point dividing a line segment in a given ratio between a fixed point and a moving point of a quadratic surface.This paper further presents such orbit equations as ∑′ and ∑″ for seventeen quadratic surfaces and derives two important conclusions for type-preserving of quadratic surfaces.