معرفي متريك لورنتسي بر روي منيفلدها و بررسي گروههاي لي تك مدولي لورنتسي سه بعدي

The introduction of lorentzian metrics on manifolds and survey of three-dimensional unimodular lorentzian lie groups

In this reaserch, first of all, for a Manifold M, using scalar product of tangent space tmM wich we show it with gm, we introduce a lorentzian metric that is in the form of g(m) = gm and endowes special features. Then, we call each lie group that has a left invariant lorentzian Metric with a lorentzian lie group. Therefore we represent a Modular function for a lie group and call a lie group with A = 1 by an unimodular lie group and following we define an unimodular lie algebra, in the end we study that under isomorphism there are only six distinct three - dimensional unimodular lorentzian lie algebras and we deal with their introduction.