Katrin FAESSLER

“Logarithmic coordinates”
(z, t) =
where (ξ, ψ, η) ∈ R × (− π π
2 , 2 ) × R.
i cos ψe ξ+i(ψ−3η)
2 , − sin ψe ξ
,
Simple description of Korányi spheres ξ = 2 ln ((z, t)H).
Derived from coordinates on H 2 C which extend to ∂H2 C (Platis)
◮ η = 0: boundary of “standard flat pack”
◮ ψ = 0: plane C × {0}
◮ ξ = 0: Korányi unit sphere
Related to the spherical coordinates (z, t) = (r cos1/2 θeiφ , r 2 sin θ)
(Korányi, Reimann) via ξ = 2 ln r, ψ = −θ, η = 1
3 (π − θ − 2φ).
Particular horizontal curves:
Katrin Fässler (University of Helsinki) A stretch map on H 1
HCAA 2012 9 / 23