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

Details Surfaces immersed in su(N+1) Lie algebras obtained from the CP^N sigma models Surfaces immersed in su(N+1) Lie algebras obtained from the CP^N sigma models

2005-02-23

arxiv.org/abs/math/0502482v3

J.Phys. A39 (2006) 9187-9214

Mathematics

Differential Geometry

32 pages, 1 figure; changes: major revision of presentation, clarifications added

Scientific paper

10.1088/0305-4470/39/29/013

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.

Affiliated with

Also associated with

No associations

Rating

Surfaces immersed in su(N+1) Lie algebras obtained from the CP^N sigma models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Surfaces immersed in su(N+1) Lie algebras obtained from the CP^N sigma models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Surfaces immersed in su(N+1) Lie algebras obtained from the CP^N sigma models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-399142