On projective group properties of the 6D pseudo-Riemannian space

The problem of defining 2D Riemannian manifolds which admit projective motions, i. e. continuous transformation groups preserving geodesics dates back to S.Lie who considered it in [1]. In more recent times, that was A.V.Aminova who has got a complete solution to this problem [3]. For the Riemannian manifolds of dimension greater than 2 the same problem has been solved by G.Fubini [4] and A.S.Solodovnikov [5]. Note that they essentially used in their studies positive definiteness of metrics under consideration. Without this positivity condition, considering pseudo-Riemannian spaces, the problem is much more complicated and requires absolutely new method of solution. In later paper, [6] A.V.Aminova has classified all the Lorentzian manifolds of dimension ≥ 3 that admit nonhomothetic projective or affine infinitesimal transformations. In each case, there were determined the corresponding maximal projective and affine Lie algebras.