Dual quadratic differentials and entire minimal graphs in Heisenberg space

摘要

We define holomorphic quadratic differentials for spacelike surfaces with constant mean curvature in the Lorentzian homogeneous spaces L(kappa, tau) with isometry group of dimension 4, which are dual to the Abresch-Rosenberg differentials in the Riemannian counterparts E(kappa, tau), and obtain some consequences. On the one hand, we classify explicitly those surfaces in L(kappa, tau) with zero differential. On the other hand, we prove that entire minimal graphs in Heisenberg space have negative Gauss curvature.