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Lie Algebras of Projective Motions of Five-Dimensional H-Spaces \(H_{221}\) of Type {221}

Abstract

We study five-dimensional pseudo-Riemannian h-spaces \(H_{221}\) of type \(\{221\}\). Necessary and sufficient conditions are determined under which \(H_{221}\) is a space of constant (zero) curvature. Nonhomothetical projective motions in \(H_{221}\) of nonconstant curvature are found, homotheties and isometries of the indicated spaces are investigated. Dimensions, basis elements, and structure equations of maximal projective Lie algebras acting in \(H_{221}\) of nonconstant curvature are determined. As a result, the classification of h-spaces \(H_{221}\) of type \(\{221\}\) by (non-homothetical) Lie algebras of infinitesimal projective and affine transformations is obtained.

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REFERENCES

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Correspondence to A. V. Aminova or D. R. Khakimov.

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Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 12, pp. 9–22.

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Aminova, A.V., Khakimov, D.R. Lie Algebras of Projective Motions of Five-Dimensional H-Spaces \(H_{221}\) of Type {221}. Russ Math. 65, 6–19 (2021). https://doi.org/10.3103/S1066369X21120021

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  • DOI: https://doi.org/10.3103/S1066369X21120021

Keywords

  • five-dimensional pseudo-Riemannian manifold
  • h-space \(H_ {221}\) of type \(\{221\}\)
  • nonhomothetical projective motion
  • projective Lie algebra.