  We construct and investigate smooth orientable surfaces in su(N) algebras.
The structural equations of surfaces associated with Grassmannian sigma models
on Minkowski space are studied using moving frames adapted to the surfaces. The
first and second fundamental forms of these surfaces as well as the relations
between them as expressed in the Gauss-Weingarten and Gauss-Codazzi-Ricci
equations are found. The scalar curvature and the mean curvature vector
expressed in terms of a solution of Grassmanian sigma model are obtained.
