Skew-symmetric matrices and integral curves in Lorentzian spaces

We provide some existence results about integral curves of a linear vector field on 3-dimensional Lorentzian space E-1(3). Moreover we have a classification of integral curves (flow lines) of a linear vector field and the normal forms of the matrix corresponding to a mapping A in Lorentzian spaces E-1(3) and E-1(2n+1).