Geodesic
Weakly symmetric Riemannian manifolds with reductive isometry group
Sbornik. Mathematics, Tome 195 (2004) no. 4, pp. 599-614

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A classification of non-symmetric weakly symmetric Riemannian manifolds with reductive symmetry group is obtained. In particular, all compact weakly symmetric Riemannian manifolds are described. Many new examples of weakly symmetric manifolds are constructed. 
@article{SM_2004_195_4_a5,
     author = {O. S. Yakimova},
     title = {Weakly symmetric {Riemannian} manifolds with reductive isometry group},
     journal = {Sbornik. Mathematics},
     pages = {599--614},
     publisher = {mathdoc},
     volume = {195},
     number = {4},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2004_195_4_a5/}
}
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O. S. Yakimova. Weakly symmetric Riemannian manifolds with reductive isometry group. Sbornik. Mathematics, Tome 195 (2004) no. 4, pp. 599-614. http://geodesic.mathdoc.fr/item/SM_2004_195_4_a5/