  We shall discuss the class of surfaces with holomorphic right Gauss maps in
non-compact duals of compact semisimple Lie groups (e.g. SL(n,C)/SU(n)), which
contains minimal surfaces in R^n and constant mean curvature 1 surfaces in H^3.
A Weierstrass type representation formula, and a Chern-Osserman type inequality
for such surfaces are given.
