Open Access
2006 Cone metrics on the sphere and Livné’s lattices
John R. Parker
Author Affiliations +
Acta Math. 196(1): 1-64 (2006). DOI: 10.1007/s11511-006-0001-9


We give an explicit construction of a family of lattices in PU (1, 2) originally constructed by Livné. Following Thurston, we construct these lattices as the modular group of certain Euclidean cone metrics on the sphere. We give connections between these groups and other groups of complex hyperbolic isometries.


Download Citation

John R. Parker. "Cone metrics on the sphere and Livné’s lattices." Acta Math. 196 (1) 1 - 64, 2006.


Received: 20 May 2005; Revised: 21 October 2005; Published: 2006
First available in Project Euclid: 31 January 2017

zbMATH: 1100.57017
MathSciNet: MR2237205
Digital Object Identifier: 10.1007/s11511-006-0001-9

Rights: 2006 © Springer-Verlag

Vol.196 • No. 1 • 2006
Back to Top