Geodesic
On various types of homogeneous Riemannian spaces with an~isotropy group which decomposes
Matematičeskie zametki, Tome 5 (1969) no. 3, pp. 361-372

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Homogeneous Riemannian spaces are considered whose isotropy group $H$ decomposes into the direct product of irreducible subgroups and the identity operator acting in mutually orthogonal planes in the tangent space of a point $M$. We exclude the special cases when an irreducible subgroup in the decomposition of $H$ is semisimple and acts on a plane whose dimension is a multiple of four. These spaces admit a rigid tensor structuref satisfying the condition $f^3+f=0$. 
@article{MZM_1969_5_3_a10,
     author = {V. E. Mel'nikov},
     title = {On various types of homogeneous {Riemannian} spaces with an~isotropy group which decomposes},
     journal = {Matemati\v{c}eskie zametki},
     pages = {361--372},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_5_3_a10/}
}
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V. E. Mel'nikov. On various types of homogeneous Riemannian spaces with an~isotropy group which decomposes. Matematičeskie zametki, Tome 5 (1969) no. 3, pp. 361-372. http://geodesic.mathdoc.fr/item/MZM_1969_5_3_a10/