  This thesis mainly treats two developments of the classical theory of
hypersurfaces inside pseudo-Riemannian space forms.
  The former - a joint work with Francesco Bonsante - consists in the study of
immersions of smooth manifolds into holomorphic Riemannian space forms of
constant curvature -1 (including SL(2,C) with a multiple of its Killing form):
this leads to a Gauss-Codazzi theorem, it suggests an approach to holomorphic
transitioning of immersions into pseudo-Riemannian space forms, a trick to
construct holomorphic maps into the PSL(2,C)-character variety, and leads to a
restatement of Bers theorem.
  The latter - a joint work with Andrea Seppi - consists in the study of
immersions of n-manifolds inside the space of geodesics of the hyperbolic
(n+1)-space. We give a characterization, in terms of the para-Sasaki structure
of this space of geodesics, of the Riemannian immersions which turn out to be
Gauss maps of equivariant immersions into the hyperbolic space.
