Manifolds with almost contact 3-structure and metrics of Hermitian–Norden type

Abstract

It is considered a differentiable manifold equipped with a pseudo-Riemannian metric and an almost contact 3-structure so that an almost contact metric structure and two almost contact B-metric structures are generated. There are introduced the so-called associated Nijenhuis tensors for the studied structures. It is given a geometric interpretation of the vanishing of these tensors as a necessary and sufficient condition for the existence of linear connections with totally skew-symmetric torsions preserving the structure. An example of a 7-dimensional manifold with connections of the considered type is given.2010 Mathematics Subject Classification. Primary 53C05, 53C15; Secondary 53C50, 53C26.