Geodesic
Riemannian manifolds in which certain curvature operator has constant eigenvalues along each helix
Archivum mathematicum, Tome 35 (1999) no. 2, pp. 129-140.

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Riemannian manifolds for which a natural skew-symmetric curvature operator has constant eigenvalues on helices are studied. A local classification in dimension three is given. In the three dimensional case one gets all locally symmetric spaces and all Riemannian manifolds with the constant principal Ricci curvatures $r_1 = r_2 = 0, r_3 \ne 0$, which are not locally homogeneous, in general.
Classification : 53C15, 53C20, 53C21, 53C22
Keywords: helix; constant eigenvalues of the curvature operator; locally symmetric spaces; curvature homogeneous spaces 
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     author = {Alexieva, Yana and Ivanov, Stefan},
     title = {Riemannian manifolds in which certain curvature operator has constant eigenvalues along each helix},
     journal = {Archivum mathematicum},
     pages = {129--140},
     publisher = {mathdoc},
     volume = {35},
     number = {2},
     year = {1999},
     mrnumber = {1711665},
     zbl = {1054.53058},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1999__35_2_a3/}
}
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Alexieva, Yana; Ivanov, Stefan. Riemannian manifolds in which certain curvature operator has constant eigenvalues along each helix. Archivum mathematicum, Tome 35 (1999) no. 2, pp. 129-140. http://geodesic.mathdoc.fr/item/ARM_1999__35_2_a3/