Canonical surfaces associated with projectors in Grassmannian sigma models

Hussin, V.; Yurdusen, I.; Zakrzewski, W.J.

doi:10.1063/1.3486690

Canonical surfaces associated with projectors in Grassmannian sigma models

Hussin, V.; Yurdusen, I.; Zakrzewski, W.J.

Authors

V. Hussin

I. Yurdusen

W.J. Zakrzewski

Abstract

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.

Citation

Hussin, V., Yurdusen, I., & Zakrzewski, W. (2010). Canonical surfaces associated with projectors in Grassmannian sigma models. Journal of Mathematical Physics, 51(10), Article 103509. https://doi.org/10.1063/1.3486690

Journal Article Type	Article
Publication Date	Oct 1, 2010
Deposit Date	Nov 23, 2010
Publicly Available Date	Oct 9, 2012
Journal	Journal of Mathematical Physics
Print ISSN	0022-2488
Electronic ISSN	1089-7658
Publisher	American Institute of Physics
Peer Reviewed	Peer Reviewed
Volume	51
Issue	10
Article Number	103509
DOI	https://doi.org/10.1063/1.3486690
Keywords	Algebra, Axiomatic field theory, Nonlinear field theory, Topology.

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Copyright Statement
Copyright 2010 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Hussin, V. and Yurdusen, I. and Zakrzewski, W.J. (2010) 'Canonical surfaces associated with projectors in Grassmannian sigma models.', Journal of mathematical physics., 51 (10). p. 103509 and may be found at http://dx.doi.org/10.1063/1.3486690