Riemannian manifolds in which certain curvature operator has constant eigenvalues along each helix

Alexieva, Yana   ; Ivanov, Stefan

Archivum mathematicum, Tome 35 (1999) no. 2, pp. 129-140

Abstract (VO)

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.

Détail

Classification : 53C15, 53C20, 53C21, 53C22
Keywords: helix; constant eigenvalues of the curvature operator; locally symmetric spaces; curvature homogeneous spaces

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