On projective motions of 5-dimensional spaces II. H-spaces of the type {41}

We study five-dimensional pseudo-Riemannian manifolds that admit non-homothetic infinitesimal projective transformations. A similar problem for 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-normalframe (Aminova), five-dimensional spaces of type {41} are defined and necessary and sufficient conditions forthe existence of projective motions of the same type are established.