超二次曲面的射影分类和仿射分类

Projective Classification and Affine Classification of the Quadric Hypersurfaces

本文给出超二次曲面的一个新的分类方法并且证明了如下的定理:Ⅰ.在 n 维射影空间中,超二次曲面的射影分类的种数为1/4(n^2+6n+4)+(1-(-1)~n)/8Ⅱ.在 n 维仿射空间中,超二次曲面的仿射分类的种数为 n^2+3n+1.

This paper gives a new method of classification of quadric hypersurfaees and proves the following theorems: Ⅰ.In the n-dimensional projective space,there are 1/4(n^2+6n+4)+(1-(-1)/8) kinds of quadric hypersurfaces accor- ding to the projective classification. Ⅱ.In the n-dimensional affine spa- ce,there are n^2+3n+1 kinds of quadric hypersurfaees accor- dins to the affine classification.