Normal almost contact metric manifolds of dimension three. (English) Zbl 0605.53018

Let (M,g) be a Riemannian manifold with an almost contact metric structure (\(\phi\),\(\xi\),\(\eta\),g). This paper is devoted to the study of such structures on three-dimensional manifolds which are in addition normal, that is \([\phi,\phi]+2\xi \oplus d\eta =0\), where [\(\phi\),\(\phi\) ] is the Nijenhuis torsion of \(\phi\). The author determines the local structure of such manifolds and studies the Riemannian curvature of (M,g). Finally, he also considers the case of three-dimensional manifolds of constant curvature equipped with such a structure. Appropriate examples are given.
Reviewer: L.Vanhecke


53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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