On the properties of the projective Lie algebras of rigid h-spaces H32 of the type {32}

A.V. Aminova^∗ , D.R. Khakimov^∗∗

Kazan Federal University, Kazan, 420008 Russia

E-mail: ^∗asya.aminova@kpfu.ru, ^∗∗dzhamoliddink@mail.ru

Received December 13, 2019

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DOI: 10.26907/2541-7746.2020.2.111-119

For citation: Aminova A.V., Khakimov D.R. On the properties of the projective Lie algebras of rigid h-spaces H₃₂ of the type {32}. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2020, vol. 162, no. 2, pp. 111–119. doi: 10.26907/2541-7746.2020.2.111-119. (In Russian)

Abstract

The five-dimensional pseudo-Riemannian spaces that admit infinitesimal projective transformations were studied. A general solution of the Eisenhart equation in the h-space H₃₂ of non-constant curvature was found. Necessary and sufficient conditions were established for the existence of a non-homothetic projective motion in the h-space H₃₂ of non-constant curvature, and, as a consequence, the structure of the non-homothetic projective Lie algebra in this space was determined.

Keywords: five-dimensional pseudo-Riemannian manifold, rigid h-space of type {32}, Eisenhart equation, projective Lie algebra

References

1. Aminova A.V. Proektivnye preobrazovaniya psevdorimanovykh mnogoobrazii [Projective Transformations of Pseudo-Riemannian Manifolds]. Moscow, Yanus-K, 2003. 619 p. (In Russian)
2. Aminova A.V. Lie algebras of infinitesimal projective transformations of Lorentz manifolds. Russ. Math. Surv., 1995, vol. 50, no. 1, pp. 69–143. doi: 10.1070/RM1995v050n01ABEH001691.
3. Aminova A.V., Khakimov D.R. On projective motions of 5-dimensional spaces I. H-spaces of the type {32}. Prostranstvo, Vremya, Fundam. Vzaimodeistviya, 2018, no. 4, pp. 21–31. doi: 10.17238/issn2226-8812.2018.4.21-31. (In Russian)

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