An example of Riemannian manifolds satisfying $R(X,\,Y)\cdot R=0$ but not $\nabla R=0$
Takagi, Hitoshi
Tohoku Math. J. (2), Tome 24 (1972) no. 4, p. 105-108 / Harvested from Project Euclid
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Publié le : 1972-05-14
Classification:  53C20 
@article{1178241595,
     author = {Takagi, Hitoshi},
     title = {An example of Riemannian manifolds satisfying $R(X,\,Y)\cdot R=0$ but not $\nabla R=0$},
     journal = {Tohoku Math. J. (2)},
     volume = {24},
     number = {4},
     year = {1972},
     pages = { 105-108},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1178241595}
}

Takagi, Hitoshi. An example of Riemannian manifolds satisfying $R(X,\,Y)\cdot R=0$ but not $\nabla R=0$. Tohoku Math. J. (2), Tome 24 (1972) no. 4, pp.  105-108. http://gdmltest.u-ga.fr/item/1178241595/