2015/02/10 by Ferreira, Maria João, Simões, Bruno Ascenso
#Differential Geometry (math.DG) #FOS: Mathematics #Primary 58E20 #Secondary 53C43
paper · doi:10.48550/arxiv.1502.02907
In [5], together with J. C. Wood, the authors gave a completely explicit formula for all harmonic maps from 2-spheres to the unitary group U(n) in terms of freely chosen meromorphic functions on S2. The simplest harmonic maps are the isotropic ones. Using Morse theory Burstall and Guest [1] showed that the harmonic maps come in clusters labeled by the isotropic ones. In this work, using the formula for harmonic maps aforementioned, we describe explicitly this procedure, showing how all harmonic maps can be built from the isotropic ones. [1] F.~E. Burstall and M.~A. Guest, Harmonic two-spheres in compact symmetric spaces, revisited, Math. Ann. 309 (1997) 541--572. [5] M.~J. Ferreira, B.~A Simões and J.~C. Wood All harmonic 2-spheres in the unitary group, completely explicitly, Math. Z. \bf 266 (2010), 953--978.