A Volume Function for CR Tetrahedra
Metric Geometry
2009-07-15 v1
Abstract
We define a volume function on configurations of four points in the 3-sphere which is invariant under the action of PU(2,1), the automorphism group of the CR structure defined on the sphere by its embedding in complex 2-space. We show that the volume function, constructed using appropriate combinations of the dilogathm function of Bloch-Wigner, satisfies a five term relation in a more general context which includes at the same time CR and real hyperbolic geometry.
Cite
@article{arxiv.0907.2305,
title = {A Volume Function for CR Tetrahedra},
author = {Elisha Falbel},
journal= {arXiv preprint arXiv:0907.2305},
year = {2009}
}