Surfaces immersed in su(N+1) Lie algebras obtained from the CP^N sigma models
Grundland, A. M. ; Strasburger, A. ; Zakrzewski, W. J.
arXiv, 0502482 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-02-23
Classification:  Mathematics - Differential Geometry,  Mathematical Physics 
@article{0502482,
     author = {Grundland, A. M. and Strasburger, A. and Zakrzewski, W. J.},
     title = {Surfaces immersed in su(N+1) Lie algebras obtained from the CP^N sigma
  models},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0502482}
}

Grundland, A. M.; Strasburger, A.; Zakrzewski, W. J. Surfaces immersed in su(N+1) Lie algebras obtained from the CP^N sigma
  models. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0502482/