不可积类光Killing矢量场是广义相对论关注的一类有连续对称性的时空 上反映其对称性的矢量场. 本文由积分子流形的概念出发, 说明矢量场可积与 其余矢场满足Pfa?方程等价. 通过选取不可积类光Killing矢量场的适配标架, 本文得到它的可积性函数, 两个可积性外微分式, 和时空上曲率确定的二维超 曲面这些时空内禀性质. 最后这些结果应用在两个含类光Killing矢量场时空的 实例上.

A twisting Killing vector ?eld of light type re?ects the continuous symmetry of its underlying spacetime which is concerned in general relativity. Based on the concept of integral-submanifold, we explain integrability of a vector ?eld is equivalent to its dual vector ?eld’s Pfa? equation. Using the adapter frame of the twisting null Killing vector ?eld, we obtain its integrability function, exterior di?erential forms, and two-dimensional hyper-surfaces with speci?ed curvature tensor, all of whom re?ect the nature of space-time. We make these results again under two speci?c space-times admitting Killing vector ?eld of light type at the end of this article.