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We prove a general local rigidity theorem for pull-backs of homogeneous formson reductive symmetric spaces under representations of discrete groups. Oneapplication of the theorem is that the volume of a closed manifold locallymodelled on a reductive homogeneous space $G/H$ is constant under deformationof the $G/H$-structure. The proof elaborates on an argument given by Labouriefor 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''.

Chern-Simons theory and cohomological invariants of representation varieties