Neighbourhoods of independence and associated geometry in manifolds of bivariate Gaussian and Freund distributions

Khadiga Arwini; Christopher Dodson

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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 $ξ$ .