On canonical-type connections on almost contact complex Riemannian manifolds

Abstract

We consider a pair of smooth manifolds, which are the counterparts in the even-dimensional and odd-dimensional cases. They are separately an almost complex manifold with Norden metric and an almost contact manifolds with B-metric, respectively. They can be combined as the so-called almost contact complex Riemannian manifold. This paper is a survey with additions of results on differential geometry of canonical-type connections (i.e. metric connections with torsion satisfying a certain algebraic identity) on the considered manifolds.

arXiv comment16 pages, a survey with additions

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Cited by in corpus (5)

• Pair of associated Schouten-van Kampen connections adapted to an almost contact B-metric structure
• Associated Nijenhuis Tensors on Manifolds with Almost Hypercomplex Structures and Metrics of Hermitian-Norden Type
• On Geometry of Manifolds with Some Tensor Structures and Metrics of Norden Type
• Invariant Tensors under the Twin Interchange of Norden Metrics on Almost Complex Manifolds
• Natural Connections with Totally Skew-Symmetric Torsion on Manifolds with Almost Contact 3-Structure and Metrics of Hermitian-Norden Type