Surfaces immersed in su ( N + 1 ) Lie algebras obtained from the C P N sigma models

We study some geometrical aspects of two dimensional orientable surfaces arrising from the study of CPN sigma models. To this aim we employ an identification of RN(N+2) with the Lie algebra su(N + 1) by means of which we construct a generalized Weierstrass formula for immersion of such surfaces. The structural elements of the surface like its moving frame, the Gauss-Weingarten and the Gauss-Codazzi-Ricci equations are expressed in terms of the solution of the CPNmodel defining it. Further, the first and second fundamental forms, the email address: [email protected] email address: [email protected] email address: [email protected]