PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 61(75), pp. 105--113 (1997)
Normal flows and harmonic manifolds
J. C. González-Dávila and L. VanheckeDepartamento de Matemática Fundamental, Universidad de La Laguna, La Laguna, Spain and Department of Mathematics, Katholieke Universiteit Leuven, Leuven, Belgium
Abstract: 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.
Keywords: Harmonic manifolds, 2-stein spaces, normal flows.
Classification (MSC2000): 53C25
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© 2001 Mathematical Institute of the Serbian Academy of Science and Arts