THE GEODESIC CURVES ON THE OSCILLATOR GROUP OF DIMENSION FOUR

Abstract

Our work is study the geometry of oscillator groups, they are the only non commutative simply connected solvable Lie groups which have a biinvariant Lorentzian metric. The oscillator group has been generalized to one dimension equals , and several aspects of its geometry have been intensively studied, both in differential geometry and in mathematical physics. In this paper, we find geodesic curves on the oscillator group of dimension four.