Canonical surfaces associated with projectors in Grassmannian sigma models


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

JOURNAL OF MATHEMATICAL PHYSICS, cilt.51, 2010 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 51 Konu: 10
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1063/1.3486690
  • Dergi Adı: JOURNAL OF MATHEMATICAL PHYSICS

Özet

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]