  In the previous paper, Takahasi and the authors generalized the theory of
minimal surfaces in Euclidean n-space to that of surfaces with holomorphic
Gauss map in certain class of non-compact symmetric spaces. It also includes
the theory of constant mean curvature one surfaces in hyperbolic 3-space.
Moreover, a Chern-Osserman type inequality for such surfaces was shown. Though
its equality condition is not solved yet, the authors have noticed that the
equality condition of the original Chern-Osserman inequality itself is not
found in any literature except for the case n=3, in spite of its importance. In
this paper, a simple geometric condition for minimal surfaces that attains
equality in the Chern-Osserman inequality is given. The authors hope it will be
a useful reference for readers.
