Geodesic
On projective motions of five-dimensional spaces of special form
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2017), pp. 97-102.

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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.
Keywords: five-dimensional pseudo-Riemannian manifold, projective motion, $h$-space of the type $\{221\}$. 
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A. V. Aminova; D. R. Khakimov. On projective motions of five-dimensional spaces of special form. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2017), pp. 97-102. http://geodesic.mathdoc.fr/item/IVM_2017_5_a10/

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