Description of surfaces associated with Grassmannian sigma models on Minkowski space
Differential Geometry
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
We construct and investigate smooth orientable surfaces in su(N) algebras. The structural equations of surfaces associated with Grassmannian sigma models on Minkowski space are studied using moving frames adapted to the surfaces. 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 scalar curvature and the mean curvature vector expressed in terms of a solution of Grassmanian sigma model are obtained.
Keywords
Cite
@article{arxiv.math/0501200,
title = {Description of surfaces associated with Grassmannian sigma models on Minkowski space},
author = {A. M. Grundland and L. Snobl},
journal= {arXiv preprint arXiv:math/0501200},
year = {2007}
}
Comments
17 pages