A curvature identity on a 6-dimensional Riemannian manifold and its applications

Yunhee Euh; Jeong Hyeong Park; Kouei Sekigawa

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Harmonic maps from a Riemannian manifold with a pole into an Hadamard manifold with negative sectional curvatures.

Atsushi Tachikawa (1992)

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Normal flows and harmonic manifolds.

González-Dávila, J.C., Vanhecke, Lieven (1997)

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Contact manifolds, harmonic curvature tensor and $(k, μ)$ -nullity distribution

Basil J. Papantoniou (1993)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we give first a classification of contact Riemannian manifolds with harmonic curvature tensor under the condition that the characteristic vector field $ξ$ belongs to the $(k, μ)$ -nullity distribution. Next it is shown that the dimension of the $(k, μ)$ -nullity distribution is equal to one and therefore is spanned by the characteristic vector field $ξ$ .