Geodesic
Normal Flows and Harmonic Manifolds
Publications de l'Institut Mathématique, _N_S_61 (1997) no. 75, p. 105

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Zbl
We prove that a $2$-stein space equipped with a non-vanishing vector field $\xi$ such that the $\xi$-sectional curvature is pointwise constant is a space of constant sectional curvature. From this it then follows that a harmonic space equipped with a unit Killing vector field such that its flow is normal, has constant sectional curvature.
Classification : 53C25
Keywords: Harmonic manifolds, 2-stein spaces, normal flows. 
J. C. González-Dávila; L. Vanhecke. Normal Flows and Harmonic Manifolds. Publications de l'Institut Mathématique, _N_S_61 (1997) no. 75, p. 105 . http://geodesic.mathdoc.fr/item/PIM_1997_N_S_61_75_a12/
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     author = {J. C. Gonz\'alez-D\'avila and L. Vanhecke},
     title = {Normal {Flows} and {Harmonic} {Manifolds}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {105 },
     year = {1997},
     volume = {_N_S_61},
     number = {75},
     zbl = {0885.53049},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1997_N_S_61_75_a12/}
}
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