Harmonic maps and constant mean curvature surfaces in H 2 x R
Harmonic maps and constant mean curvature surfaces in H 2 x R
We introduce a hyperbolic Gauss map into the Poincar´e disk for any surface in H2×R with regular vertical projection, and prove that if the surface has constant mean curvature H = 1/2, this hyperbolic Gauss map is harmonic. Conversely, we show that every nowhere conformal harmonic map from an open …