三维Minkowski空间中二次曲面的分类

Classification of Quadratic Surfaces in 3D Minkowski Space

研究了二次曲面绕不同坐标轴旋转后再进行平移变换下的不变量,根据这些不变量来研究二次曲面的等价类,达到分类的目的.在三维Minkowski空间中,二次曲面的变换有旋转和平移,旋转又分为在正交标架下绕类空轴、类时轴的旋转和在伪正交标架下绕类光轴的旋转,在不同的旋转变换下有不同的不变量,分类结果也不同.

Discusses the invariants of quadratic surfaces after they rotate around different coordinate axes then translate parallel in the three dimensional Minkowski space. According to these invariants, the equivalent classes of the quadratic surfaces are defined for classification. It is revealed that in the 3D Minkowski space the transformation of quadratic surface includes around both parallel translation and rotation which comprises space-like and time-like axes within orthogonal frame and that around null-like axes within pseudo-orthogonal frame, where different rotation transformation results in different invariants and classification.