Constant curvature solutions of Grassmannian sigma models: (1)   Holomorphic solutions
  We present a general formula for the Gaussian curvature of curved holomorphic 2-spheres in Grassmannian manifolds G(m, n). We then show how to construct such solutions with constant curvature. We also make some relevant conjectures for the admissible constant curvatures in G(m, n) and give some explicit expressions, in particular, for G(2, 4) and G(2, 5). 
Laurent Delisle, Veronique Hussin and Wojtek J. Zakrzewski
math-ph math.MP