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Q: Do there exist theorems of de Sitter geometry, just as there are theorems of Minkowski and anti-de Sitter geometry?

wladThere are theorems of Euclidean, hyperbolic, elliptic and Minkowski geometry. I'm wondering about planar de Sitter geometry. Regarding planar anti-de Sitter geometry, based on my understanding of Cayley-Klein models, the theorems of planar anti-de Sitter geometry are the same as those of planar h...

In mathematics, a Cayley–Klein metric is a metric on the complement of a fixed quadric in a projective space which is defined using a cross-ratio. The construction originated with Arthur Cayley's essay "On the theory of distance" where he calls the quadric the absolute. The construction was developed in further detail by Felix Klein in papers in 1871 and 1873, and subsequent books and papers. The Cayley–Klein metrics are a unifying idea in geometry since the method is used to provide metrics in hyperbolic geometry, elliptic geometry, and Euclidean geometry. The field of non-Euclidean geometry...
 

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