抄録
We show that a non-conformal harmonic map from a Riemann surface into the Euclidean n-sphere can be considered as a component of minimal surfaces in higher dimensional spheres. In the same principle, we show that the generalized Gauss map of constant mean curvature surfaces in the 3-sphere globally splits into two non-confirmal harmonic maps into 2-sphere. Using this, we obtain ezamples of non-trivial harmonic map deformations for compact Riemann durfaces of arbitrary positive genus. In particular, we give a lower bound for the nullity(as harmonic maps)of the feneralized Gauss map of compact CMC surfaces in the 3-sphere. Furthermore, we obtain an affirmative answer to Lawson's conjectire for superconformal minimal surfaces in 4m-spheres.
