Chern-Simons forms of pseudo-Riemannian homogeneity on the oscillator group

We consider forms of Chern-Simons type associated to homogeneous pseudo-Riemannian structures. The corresponding secondary classes are a measure of the lack of a homogeneous pseudo-Riemannian space to be locally symmetric. In the present paper, we compute these forms for the oscillator group and the corresponding secondary classes of the compact quotients of this group.