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

Olszak, Zbigniew

Ann. Pol. Math. 47, 41-50 (1986).

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.)

Keywords:

almost contact structure; Nijenhuis torsion; Riemannian curvature; constant curvature