A Volume Function for CR Tetrahedra

Details A Volume Function for CR Tetrahedra A Volume Function for CR Tetrahedra

2009-07-14

arxiv.org/abs/0907.2305v1

Mathematics

Metric Geometry

Scientific paper

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.

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