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

2012/04/02 by Laurent Delisle, L. Delisle, Veronique Hussin +3 · 2 citations
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Waves and Solitons #math-ph #math.MP

paper · pdf · doi:10.1016/j.geomphys.2013.01.003

published as Journal of Geometry and Physics vol. 66 (2013), pp. 24-36 · 14 pages

arxiv created 2012/04/02 · openalex publication_date 2013/01/14 · arxiv updated 2013/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Abstract

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).

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