On the existence of almost contact structure and the contact magnetic field

Abstract

In this short note we give a simple proof of the existence of an almost contact metric structure on any orientable 3-dimensional Riemannian manifold (M3, 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 of 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.