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Abstract  

We give a simple proof of the existence of an almost contact metric structure on any orientable 3-dimensional Riemannian manifold (M 3, g) with the prescribed metric g as the adapted metric of the almost contact metric structure. By using the key formula for the structure tensor obtained in the proof this theorem, we give an application which allows us to completely determine the magnetic flow of the contact magnetic field in any 3-dimensional Sasakian manifold.

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In this paper geodesically corresponding metricsg and on a manifoldM, dim ≥5, under the assumption that the tensorsR andS of the metricg satisfyR.R=Q(S, R), are considered. It is stated that the corresponding tensors and of not necessarily must satisfy . Certain relations between the curvatures ofg and are obtained.

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