Chern-Simons forms of pseudo-Riemannian homogeneity on the oscillator group (Q1415152)

The authors compute the Chern-Simons forms for left-invariant pseudo-Riemannian metrics on the 4-dimensional oscillator group. The corresponding secondary cohomology classes measure how far a homogeneous space is from being locally symmetric. In the paper these classes are computed for certain compact quotients of the oscillator group by discrete subgroups. For a particular choice of parameters the classes vanish.