Geodesic
Holonomy groups of four-dimensional pseudo-Riemann spaces
Matematičeskie zametki, Tome 9 (1971) no. 1, pp. 59-66

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Four-dimensional pseudo-Riemann spaces $\mathcal{V}^4$ 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 spaces $\mathcal{V}^4$: 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. 
@article{MZM_1971_9_1_a7,
     author = {V. V. Astrakhantsev},
     title = {Holonomy groups of four-dimensional {pseudo-Riemann} spaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {59--66},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_9_1_a7/}
}
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V. V. Astrakhantsev. Holonomy groups of four-dimensional pseudo-Riemann spaces. Matematičeskie zametki, Tome 9 (1971) no. 1, pp. 59-66. http://geodesic.mathdoc.fr/item/MZM_1971_9_1_a7/