## 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

### MSC:

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