应用不变量化简四维欧式空间中二次曲面的方程

Simplification for the Equation of Quadratic Surface in Four-Dimensional Euclidean Space with Invariant

利用四维欧式空间中二次曲面的5个不变量和3个半不变量取值的不同情形,给出了在四维欧式空间中二次曲面的6种类型简化方程的一般形式,并给出了相应算例。

The study of the invariant of quadratic surface has become a very important central problem in analytic geometry. Based on the values of five invariants and three semi invariants of quadratic surface in four-dimensional Euclidean space in different situations, six types general forms of the simplified equation of quadratic surface in four-dimensional Euclidean space are given in this paper, and the corresponding examples are also given.