A VOLUME FUNCTION FOR SPHERICAL CR TETRAHEDRA

We define a volume function on configurations of four points in the sphere S³ which is invariant under the action of PU(2, 1), the automorphism group of the CR structure defined on S³ by its embedding in ℂ². We show that the volume function, constructed using appropriate combinations of the dilogarithm 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.