SPACE, TIME AND FUNDAMENTAL INTERACTIONS

ON PROJECTIVE MOTIONS OF 5-DIMENSIONAL SPACES II. H-SPACES OF THE TYPE {41}

Aminova A.V., Khakimov D.R.

We study five-dimensional pseudo-Riemannian manifolds (M,g) that admit non-homothetic infinitesimal projective transformations. A similar problem for n-dimensional proper Riemannian and Lorentzian spaces was solved by T. Levi-Civita, A.Z. Petrov, A.S. Solodovnikov, and A.V. Aminova. For pseudo-Riemannian manifolds of arbitrary signature and dimension the problem of their classification on algebras and Lie groups of projective transformations, set over a hundred years ago, remains open. In this paper, using the method of the skew-normal frame (Aminova), five-dimensional h-spaces of type {41} are defined and necessary and sufficient conditions for the existence of projective motions of the same type are established.