Description of surfaces associated with $CP^{N-1}$ sigma models on Minkowski space

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dc.creatorGrundland, A. M.
dc.creatorSnobl, L.
dc.date2004-05-26
dc.date2004-11-08
dc.date.accessioned2026-07-07T06:19:19Z
dc.date.available2026-07-07T06:19:19Z
dc.descriptionThe objective of this paper is to construct and investigate smooth orientable surfaces in $R^{N^2-1}$ by analytical methods. The structural equations of surfaces in connection with $CP^{N-1}$ sigma models on Minkowski space are studied in detail. This is carried out using moving frames adapted to surfaces immersed in the $su(N)$ algebra. The first and second fundamental forms of this surface as well as the relations between them as expressed in the Gauss-Weingarten and Gauss-Codazzi-Ricci equations are found. The Gaussian curvature, the mean curvature vector and the Willmore functional expressed in terms of a solution of $CP^{N-1}$ sigma model are obtained. An example of a surface associated with the $CP^1$ model is included as an illustration of the theoretical results.
dc.description19 pages, 1 figure; shorter version, some typos and minor mistakes corrected
dc.identifierhttps://arxiv.org/abs/math/0405513
dc.identifierhttp://arxiv.org/abs/math/0405513
dc.identifierJournal of Geometry and Physics 56 (2006) 512-531
dc.identifierdoi:10.1016/j.geomphys.2005.03.003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95031
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.subject70H06; 53A05
dc.titleDescription of surfaces associated with $CP^{N-1}$ sigma models on Minkowski space
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