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Статья
2019

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


A. V. AminovaA. V. Aminova, D. R. KhakimovD. R. Khakimov
Русская математика
https://doi.org/10.3103/S1066369X19100098
Abstract / Full Text

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).

Author information
  • Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008, RussiaA. V. Aminova & D. R. Khakimov
References
  1. Aminova, A.V. Projective transformations of pseudo-Riemannian manifolds (Janus-K, Moscow, 2003) [in Russian].
  2. Aminova, A.V. “Lie algebras of infinitesimal projective transformations of Lorentz manifolds”, Russian Mathematical Surveys50(1), 69–143 (1995).
  3. Aminova, A.V., Khakimov, D.R. “On projective motions of five-dimensional spaces of special form”, Russian Mathematics61(5), 83–87 (2017).
  4. Schur, F. Schur, F. “Über den Zusammenhang der Räume konstanter Krümmungsmasses mit den projectiven Raumen”, Math. Ann.27, 537–567 (1886).