We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Durham University

Department of Mathematical Sciences


Publication details for Professor Emeritus Wojtek Zakrzewski

Hussin, V., Yurdusen, I. & Zakrzewski, W.J. (2010). Canonical surfaces associated with projectors in Grassmannian sigma models. Journal of Mathematical Physics 51(10): 103509.

Author(s) from Durham


We discuss the construction of higher-dimensional surfaces based on the harmonic maps of S2 into PN−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.