展形的Klein表示

THE KLEIN'S REPRSENTATION OF SPREAD

本文给出ＰＧ（３．ｑ）（ｑ≥＝５是奇数）的半二阶曲面和正则展形在ＰＧ（５．ｑ）中的表示集的构图性质．证明了１、ＰＧ（３．ｑ）中的ｑ＋１条线构成半二阶曲面的充要条件是它在ＰＧ（５．ｑ）中的表示集是一二阶曲线。２、ＰＧ（３．ｑ）中的ｑ２＋１条线的构成正则展形的充要条件是它在ＰＧ（５．ｑ）中的表示集是一椭圆型二阶曲面。

The paper showed the configurational properties of the Klein's representation in PG (5,q) of the regulus and regular spread of PG (3,q ) { (q≥5) is a odd integer}. The results that we have ever proved are as follows:①The q+1 lines of PG(3,q) is a regulus if and only if the Klein's representation in PG (5,q) is a conic.② The q2+ 1 lines of PG(3,q) is a regular spread if and only if the Klein's representation in PG(5,q) is a quadrics.