Geometry of oscillator groups and locally symmetric manifolds (Q1771167)

The authors exhibit new locally symmetric structures on the oscillator manifolds. These structures are obtained from explicit pseudo-Riemannian, locally symmetric, left invariant metrics and from affine structures on the oscillator groups in the sense of [\textit{A. Medina} and \textit{P. Revoy}, Manuscr. Math. 52, 81--95 (1985; Zbl 0576.53042)]. Moreover, they produce other examples of locally symmetric manifolds by the determination of the group of isometries of the oscillator groups.