Description of surfaces associated with CPN−1 sigma models on Minkowski space

The objective of this paper is to construct and investigate smooth orientable surfaces in RN2−1 by analytical methods. The structural equations of surfaces in connection with CPN−1 sigma models on Minkowski space are studied in detail. This is carried out using moving frames adapted to surfaces immersed in the su(N)su(N) algebra. 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 Gaussian curvature, the mean curvature vector and the Willmore functional expressed in terms of a solution of CPN−1 sigma model are obtained. An example of a surface associated with the CP1 model is included as an illustration of the theoretical results.