单叶双曲面直母线族性质研究补遗

对于单叶双曲面直母线的一般研究只是指出 ,单叶双曲面有两族直母线 .而且只是从将方程 x2a2 y2b2 -z2c2 =1化为 x2a2 -z2c2 =1-y2b2 出发 ,得出了u族和v族两族直母线 .一般研究并没有解决 ,单叶双曲面是否只有这两族直母线 ,从 x2a2 -z2c2 =1-y2b2 出发是否还能得出另外的直母线族 ?尤其是 ,若从 y2b2 -z2c2 =1-x2a2 出发 ,是否又会得出另外的直母线族 ?这些直母线族又与原来的u族、v族有什么关系 ?本文就是解决这些问题 ,作为对单叶双曲面直母线性质研究的补遗 .

Supplementary Study About the Character of Straight Generator Groups of Simple Double Surface

The former study about the straight generator of simple double surface pointed out that simple double surface has two groups of straight generator groups. When we change equation x 2/a 2 y 2/b 2-z 2/c 2=1 to x 2/a 2-z 2/c 2=1-y 2/b 2,we may get two groups of generators. They are U group and V group. Former study didn't explain that dose simple double surface only has two groups of generators. From equation x 2/a 2-z 2/c 2=1-y 2/b 2 can we get other straight generators? Especially that, if we start from y 2/b 2-z 2/c 2=1-x 2/a 2 can we get other straight generator groups? If there are some new groups, what is the relationship between new groups and former U group and V group? This article mainly discussed above questions, so it is a supplementary study about the character of simple double surface.