Classification of complete left-invariant affine structures on the   Oscillator group
  The goal of this paper is to provide a method, based on the theory of extensions of left-symmetric algebras, for classifying left-invariant affine structures on a given solvable Lie group of low dimension. To better illustrate our method, we shall apply it to classify complete left-invariant affine structures on the oscillator group. 
Mohammed Guediri
math.DG math.RA