Holonomy groups of four-dimensional pseudo-Riemann spaces

Four-dimensional pseudo-Riemann spacesV₁ with a metric having the signature (3, 1) are investigated. Subgroups of the Lorentz group are described which can be holonomy groups of the pseudo-Riemann spacesV: a) with zero Ricci curvature and b) symmetric. The reducibility of the above class of spaces is determined as a function of the holonomy group.Translated from Matematicheskie Zametki, Vol. 9, No.1, pp. 59–66, January, 1971.In conclusion, the author wishes to thank his scientific director D. V. Alekseevskii for his help in this work.