Canonical surfaces associated with projectors in grassmannian sigma models

Abstract

We discuss the construction of higher-dimensional surfaces based on the harmonic maps of $S^2$ into $C{P}^{N-1}$ and other grassmannians. We show that there are two ways of implementing this procedure - both based on the use of the relevant projectors. We study various properties of such projectors and show that the Gaussian curvature of these surfaces, in general, is not constant. We look in detail at the surfaces corresponding to the Veronese sequence of such maps and show that for all of them this curvature is constant but its value depends on which mapping is used in the construction of the surface.

References in corpus (4)

• On analytic descriptions of two-dimensional surfaces associated with the CP^(N-1) sigma model
• Susy CP^(N-1) model and surfaces in R^(N^2-1)
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Cited by in corpus (6)

• Constant curvature solutions of Grassmannian sigma models: (1) Holomorphic solutions
• Constant curvature solutions of Grassmannian sigma models: (2) Non-holomorphic solutions
• Constant curvature surfaces of the supersymmetric $\mathbb{C}{P}^{N-1}$ sigma model
• On the surfaces associated with $\mathbb{C}{P}^{N-1}$ models
• General solutions of the supersymmetric $\mathbb{C}{P}^2$ sigma model and its generalisation to $\mathbb{C}{P}^{N-1}$
• Unifying Geometrical Representations of Gauge Theory