Surfaces in a pseudo-sphere with harmonic or 1-type pseudo-spherical   Gauss map
  We give a complete classification of Riemannian and Lorentzian surfaces of arbitrary codimension in a pseudo-sphere whose pseudo-spherical Gauss maps are of 1-type or, in particular, harmonic. In some cases a concrete global classification is obtained, while in other cases the solutions are described by an explicit system of partial differential equations. 
Burcu Bekta\c{s}, Joeri Van der Veken, Luc Vrancken
math.DG