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Russian Mathematics

, Volume 63, Issue 10, pp 77–83 | Cite as

Projective Group Properties of h-Spaces of Type {221}

  • A. V. AminovaEmail author
  • D. R. KhakimovEmail author
Brief Communications
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Abstract

The curvature of a 5-dimensional h-space H221 of the type {221} [3] is investigated, necessary and sufficient conditions are obtained for H221 to be a space of constant curvature K (Theorem 1). A general solution of the Eisenhart equation is found in an h-space H221 of non-constant curvature. The necessary and sufficient conditions for the existence of non-homothetical projective motion in an h-space H221 of non-constant curvature are established (Theorem 5) and, as a consequence, the structure of the non-homothetical projective Lie algebra in such a space is determined (Theorem 6).

Key words

five-dimensional pseudo-Riemannian manifold the Eisenhart equation projective Lie algebra h-space of the type {221} 

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References

  1. 1.
    Aminova, A.V. Projective transformations of pseudo-Riemannian manifolds (Janus-K, Moscow, 2003) [in Russian].zbMATHGoogle Scholar
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    Aminova, A.V. “Lie algebras of infinitesimal projective transformations of Lorentz manifolds”, Russian Mathematical Surveys50(1), 69–143 (1995).MathSciNetCrossRefGoogle Scholar
  3. 3.
    Aminova, A.V., Khakimov, D.R. “On projective motions of five-dimensional spaces of special form”, Russian Mathematics61(5), 83–87 (2017).MathSciNetCrossRefGoogle Scholar
  4. 4.
    Schur, F. Schur, F. “Über den Zusammenhang der Räume konstanter Krümmungsmasses mit den projectiven Raumen”, Math. Ann.27, 537–567 (1886).CrossRefGoogle Scholar

Copyright information

© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Kazan Federal UniversityKazanRussia

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