R^(2,1)中二次曲面的化简与点的轨迹方程

Simplification of conicoids and trace equations of traces of a point in 3-Minkowski space

在R2,1中根据合同变换法将二次曲面化为标准形,并给予证明。在R2,1中讨论了任意点到定平面(直线)与到定点的距离之比等于常数的轨迹方程,并按方程中的平方项的系数的正负将其进行了分类。

Conicoids were simplified into standard shapes by the way of congruent transformation in 3-Minkowski space and its principle was proved.The trace equations of any point that the ratio is a constant,which is the radio of the distance of any point from the fixed plane(the fixed straight line) to its ditance from the fixed point in 3-Minkowski space were discussed.And the trace equations were classified by the signs of the squara coefficient in the equations.