Geodesic
Some generalizations of the Riemann spaces of Einstein
Matematičeskie zametki, Tome 16 (1974) no. 4, pp. 619-622.

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We introduce a class of Riemann structures, called generalized Einstein structures of index $2e$, of which Einstein spaces are a particular case. We show that these structures are stationary for functions introduced on a family of Riemann structures of the compact manifold of H. Weyl. This result solves a problem of M. Berger. As examples of structures which are generalized Einstein structures over all indices we cite homogeneous compact Riemann spaces with a nondecomposable isotropy group and products of such spaces. 
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     author = {G. M. Kuz'mina},
     title = {Some generalizations of the {Riemann} spaces of {Einstein}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {619--622},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {1974},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_4_a14/}
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G. M. Kuz'mina. Some generalizations of the Riemann spaces of Einstein. Matematičeskie zametki, Tome 16 (1974) no. 4, pp. 619-622. http://geodesic.mathdoc.fr/item/MZM_1974_16_4_a14/