Geometry of surfaces associated to Grassmannian sigma models

30th International Colloquium on Group Theoretical Methods in Physics

Delisle, L.^1 ; Hussin, V.^2,3 ; Zakrzewski, W.J.^4

Institut de Mathematiques de Jussieu-Paris Rive Gauche, UP7D-Campus des Grands Moulins, Batiment Sophie Germain, Cases 7012, Paris Cedex 13

75205, France^1

Departement de Mathematiques et de Statistique, Universite de Montreal, Succ. Centre-ville, C. P. 6128, Montreal (Quebec)

H3C 3J7, Canada^2

Centre de Recherches Mathematiquxes, Universite de Montreal, Succ. Centre-ville, C. P. 6128, Montreal (Quebec)

H3C 3J7, Canada^3

Department of Mathematical Sciences, University of Durham, Durham

DH1 3LE, United Kingdom^4

关键词: Gaussian curvatures;    Geometric characteristics;    Grassmannian;    Mean curvature;    Sigma model;    Topological charges;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/597/1/012029/pdf
DOI  :  10.1088/1742-6596/597/1/012029

来源: IOP

【 摘 要 】

We investigate the geometric characteristics of constant Gaussian curvature surfaces obtained from solutions of the G(m, n) sigma model. Most of these solutions are related to the Veronese sequence. We show that we can distinguish surfaces with the same Gaussian curvature using additional quantities like the topological charge and the mean curvature. The cases of G(1,n) = CPn-1and G(2,n) are used to illustrate these characteristics.