Canonical surfaces associated with projectors in Grassmannian sigma models


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Hussin V., Yurdusen İ., Zakrzewski W. J.

JOURNAL OF MATHEMATICAL PHYSICS, vol.51, no.10, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 51 Issue: 10
  • Publication Date: 2010
  • Doi Number: 10.1063/1.3486690
  • Journal Name: JOURNAL OF MATHEMATICAL PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Hacettepe University Affiliated: Yes

Abstract

We discuss the construction of higher-dimensional surfaces based on the harmonic maps of S(2) into CP(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. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3486690]