Grassmannians and conformal structure on absolutes
Differential Geometry
2020-01-27 v5
Abstract
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.
Cite
@article{arxiv.0907.4469,
title = {Grassmannians and conformal structure on absolutes},
author = {Sasha Anan'in and Eduardo C. Bento Goncalves and Carlos H. Grossi},
journal= {arXiv preprint arXiv:0907.4469},
year = {2020}
}
Comments
8 pages. Dedicated to the memory of Waldyr Rodrigues Jr