Grassmannian与绝对数上的共形结构
Grassmannians and conformal structure on absolutes
摘要：
我们研究了与具有非退化厄米形式的线性空间相关的格拉斯曼算子。这些格拉斯曼几何允许我们解释（伪）黎曼射影几何和其理想边界（绝对）上的共形结构之间的关系。这种关系包括实双曲空间绝对值上的共形结构、de Sitter空间绝对值上的共形结构、复双曲空间绝对值上的共形切触结构以及反de Sitter空间绝对值上的因果结构。
英文摘要：
We study grassmannians associated with a linear space with a nondegenerate hermitian form. The geometry of these grassmannians allows us to explain the relation between a (pseudo-)riemannian projective geometry and the conformal structure on its ideal boundary (absolute). Such relation encompasses, for instance, the usual conformal structure on the absolute of real hyperbolic space, the usual conformal structure on the absolute of de Sitter space, the conformal contact structure on the absolute of complex hyperbolic space, and the causal structure on the absolute of anti-de Sitter space.
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