Constant curvature solutions of Grassmannian sigma models: (2) Non-holomorphic solutions

TL;DR

This paper extends methods for constructing constant curvature maps from 2-spheres into Grassmannian manifolds, focusing on non-holomorphic solutions and analyzing their properties and curvature values.

Contribution

It introduces a generalized procedure for non-holomorphic solutions of Grassmannian sigma models and explores their constant curvature characteristics.

Findings

Provides explicit expressions for non-holomorphic solutions

Discusses how to construct constant curvature maps

Analyzes possible curvature values

Abstract

We generalize here our general procedure for constructing constant curvature maps of 2-spheres into Grassmannian manifolds G(m,n) this time concentrating our attention on maps which are non-holomorphic. We present some expressions describing these solutions in the general case and discuss how to use these results to construct solutions of constant curvature. We also discuss possible values of this constant curvature.