Complex lines in complex hyperbolic space H ℂ 2

Yingqing Xiao () and Yueping Jiang ()
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Yingqing Xiao: Hunan University
Yueping Jiang: Hunan University

Indian Journal of Pure and Applied Mathematics, 2011, vol. 42, issue 5, 279-289

Abstract: Abstract Let p 1, p 2, p 3, p 4 be four pairwise distinct points in the boundary of complex hyperbolic 2-space H ℂ 2 and any three points do not lie in the same C-circle. We show that we are always able to group the four points into two classes such that each class contains two points, the two complex lines spanned by each class are ultra-parallel or intersect. As an application, we can simplify the discussion in the paper [7], in which Parker and Platis used the global geometry coordinates to describe the Falbel’s cross-ratio variety of the four pairwise distinct points on the ∂H ℂ 2 .

Keywords: Complex hyperbolic space; Hermitian cross-product; C-Circle (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s13226-011-0019-3

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