Grassmannians and Conformal Structure on Absolutes
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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.
Mathematics Subject Classication53A20 (53A35, 51M10)
It was with great sadness that we heard of the passing of Professor Waldyr Rodrigues Jr. He was a dear friend and an exceptional scientist with whom we had the pleasure and the privilege to discuss many subjects related to mathematics and physics. Waldyr was very fond of natural and coordinate-free methods in geometry, a point of view that gave rise to this paper. We are very grateful to Alexei L. Gorodentsev and Nikolay A. Tyurin for their stimulating interest in this work and to the referees whose suggestions have greatly contributed to the exposition. This paper was partially developed while the first author was enjoying the hospitality of the IHES and, the third author, that of the MPIM.
- 4.Calegari, D.: Causal Geometry, Geometry and the Imagination (Blog Post at Lamington). http://wordpress.com/2009/12/10/causal-geometry (2009)