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

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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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