Geodesic
Contact manifolds, harmonic curvature tensor and $(k,\mu )$-nullity distribution
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 2, pp. 323-334

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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 $\xi $ belongs to the $(k,\mu )$-nullity distribution. Next it is shown that the dimension of the $(k,\mu )$-nullity distribution is equal to one and therefore is spanned by the characteristic vector field $\xi $.
Classification : 53C05, 53C15, 53C20, 53C21, 53C25
Keywords: contact Riemannian manifold; harmonic curvature; $D$-homothetic deformation 
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     title = {Contact manifolds, harmonic curvature tensor and $(k,\mu )$-nullity distribution},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
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Papantoniou, Basil J. Contact manifolds, harmonic curvature tensor and $(k,\mu )$-nullity distribution. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 2, pp. 323-334. http://geodesic.mathdoc.fr/item/CMUC_1993__34_2_a13/