PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 61(75), pp. 105113 (1997) 

Normal flows and harmonic manifoldsJ. C. GonzálezDávila and L. VanheckeDepartamento de Matemática Fundamental, Universidad de La Laguna, La Laguna, Spain and Department of Mathematics, Katholieke Universiteit Leuven, Leuven, BelgiumAbstract: We prove that a $2$stein space equipped with a nonvanishing 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. Keywords: Harmonic manifolds, 2stein spaces, normal flows. Classification (MSC2000): 53C25 Full text of the article:
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