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Surfaces immersed in su(N+1) Lie algebras obtained from the CP^N sigma models
We study some geometrical aspects of two dimensional orientable surfaces
arrising from the study of CP^N sigma models. To this aim we employ an
identification of R^(N(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 CP^N model defining it. Further, the first and second fundamental forms,
the Gaussian curvature, the mean curvature vector, the Willmore functional and
the topological charge of surfaces are expressed in terms of this solution. We
present detailed implementation of these results for surfaces immersed in su(2)
and su(3) Lie algebras.Comment: 32 pages, 1 figure; changes: major revision of presentation,
clarifications adde