Geometry of surfaces associated to grassmannian sigma models

TL;DR

This paper explores the geometric properties of surfaces derived from solutions to Grassmannian sigma models, focusing on their curvature, topological charge, and mean curvature to distinguish between different solutions.

Contribution

It provides a detailed analysis of the geometric features of Grassmannian sigma model surfaces, highlighting methods to differentiate solutions with identical Gaussian curvature.

Findings

Surfaces with the same Gaussian curvature can be distinguished using topological charge and mean curvature.

Most solutions are related to the Veronese sequence.

Illustrations include cases of G(1,n) and G(2,n).

Abstract

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 $G(1,n)=\mathbb{C}P^{n-1}$ and $G(2,n)$ are used to illustrate these characteristics.