开零锥中洛伦兹超曲面的几何性质

Geometric Properties of Lorentzian Hypersurfaces in Open Nullcone

开零锥中洛伦兹超曲面的研究难点在于无法利用伪外积运算从切空间中获取该超曲面的法向量.为了解决这一难题,可以借助Legendrian对偶定理的帮助.利用Legendrian对偶定理,构造了开零锥中的Lorentzian超曲面nullcone高斯像,Anti de Sitter高斯像和伪球高斯像并初步建立了开零锥中洛伦兹超曲面的的斜几何.

The difficulty in the study of Lorentzian hypersurface in open nullcone is that it is impossible to obtain the normal vector of the hypersurface from the tangent space by using pseudo wedge operation.In order to solve this problem,we need the help of the theory of Legendrian duality.In this paper,we prove the existence of the nullcone Gaussian image,the Anti de Sitter Gaussian image and the pseudo-sphere Gaussian image of Lorentzian hypersurface in open nullcone by Legendrian dual theorem,and we preliminarily establish the slant geometry of Lorentzian hypersurfaces in open nullcone.