  We prove a general local rigidity theorem for pull-backs of homogeneous forms
on reductive symmetric spaces under representations of discrete groups. One
application of the theorem is that the volume of a closed manifold locally
modelled on a reductive homogeneous space $G/H$ is constant under deformation
of the $G/H$-structure. The proof elaborates on an argument given by Labourie
for closed anti-de Sitter $3$-manifolds.
  The core of the work is a reinterpretation of old results of Cartan,
Chevalley and Borel, showing that the algebra of $G$-invariant forms on $G/H$
is generated by ``Chern-Weil forms'' and ``Chern-Simons forms''.
