Аннотация:
Together with spaces of constant sectional curvature and products of a real line with a manifold of constant curvature, the socalled Egorov spaces and $\varepsilon$-spaces exhaust the class of $n$-dimensional
Lorentzian manifolds admitting a group of isometries of dimension at least $\frac12 n(n-1)+1$, for almost all values of $n$ [Patrangenaru V., Geom. Dedicata102 (2003), 25–33]. We shall prove that the curvature tensor of these spaces satisfy several interesting algebraic properties. In particular, we will show that Egorov spaces are Ivanov–Petrova manifolds, curvature-Ricci commuting (indeed, semi-symmetric) and $\mathcal P$-spaces, and that $\varepsilon$-spaces are Ivanov–Petrova and curvature-curvature commuting
manifolds.
Ключевые слова:Lorentzian manifolds; skew-symmetric curvature operator; Jacobi, Szabó and skew-symmetric curvature operators; commuting curvature operators; IP manifolds; $\mathcal C$-spaces and $\mathcal P$-spaces.