The generalized Gauss map of a maximal surface in a Lorentzian space

The main objective of this dissertation is to explore some properties of the Gauss map of maximal surfaces. The following questions will be answered: (1) What can we tell about a totally umbilic spacelike surface? (2) What is the necessary and sufficient condition for M to be maximal in terms of Gauss map? (3) How can we generally represent a simply-connected maximal surface? (4) If the Gaussian image of a maximal surface lies in a proper subspace of CP$\sp{\rm n-1}$, how can we characterize it?