On projective motions of five-dimensional spaces of special form

The paper is devoted to the problem of determining of $5$-dimensional pseudo-Riemannian manifolds $ (M, g) $ admitting projective motions ($ h $-spaces). A similar problem for $ n $-dimensional proper Riemannian and Lorentz spaces was solved by Levi–Civita, Solodovnikov, Petrov and Aminova. For pseudo-Riemannian manifolds of arbitrary signature and dimension the problem of their classification in Lie algebras and Lie groups of projective transformations, set more than a hundred years ago, is still open. In this paper five-dimensional $ h $-spaces of the type $ \{221\} $ are determined using the method of skew-normal frame (Aminova) and necessary and sufficient conditions for the existence of projective motions of the same type are established.