  A Lie group is called orthogonal if it carries a bi-invariant pseudo
Riemannian metric. Oscillator Lie groups constitutes a subclass of the class of
orthogonal Lie groups. In this paper, we determine the Lie bialgebra structures
and the solutions of the classical Yang-Baxter equation on a generic class of
oscillator Lie groups. On the other hand, we show that any solution of the
classical Yang-Baxter equation on an orthogonal Lie group induces a metric in
the dual Lie groups associated to this solution. This metric is geodesically
complete if and only if the dual are unimodular. More generally, we show that
any solution of the generalized Yang-Baxter equation on an orthogonal Lie group
determines a left invariant locally symmetric pseudo-Riemannian metric on the
corresponding dual Lie groups. Applying this result to oscillator Lie groups we
get a large class of solvable Lie groups with flat left invariant Lorentzian
metric.
