Constant curvature solutions of Grassmannian sigma models: (1) Holomorphic solutions

We present a general procedure for constructing constant curvature holomorphic maps of 2-spheres into Grassmannian manifolds G(m,n)G(m,n). Our procedure allows us to make a couple of conjectures as to the possible values of this curvature. We prove our conjectures for G(2,4)G(2,4), G(2,5)G(2,5), present explicit formulae for the relevant maps and show that they agree with those found by other methods. We also make some comments about the maps into G(2,n)G(2,n) for n≥6n≥6.