  We consider Picard surfaces, locally symmetric varieties $S_{\Gamma}$
attached to the Lie group SU(2,1), and we construct explicit differential forms
on $S_{\Gamma}$ representing Eisenstein classes, i.e. cohomology classes
restricting non-trivially to the boundary of the Borel-Serre compactification.
This is needed for the computation of the class of the extensions of the Hodge
structure that we have constructed in [2] according to the predictions of the
Bloch-Beilinson conjectures. The tool for the construction of the differential
forms is an analysis of relative Lie algebra cohomology of the principal series
of SU(2,1) using recent methods of Buttcane and Miller.
