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arxiv: 1203.3290 · v1 · pith:GUR2XKI5new · submitted 2012-03-15 · 🧮 math.DG

Almost contact B-metric manifolds with curvature tensors of K\"ahler type

classification 🧮 math.DG
keywords tensormanifoldsahler-typealmostb-metricconnectioncontactcurvature
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On 5-dimensional almost contact B-metric manifolds, the form of any K\"ahler-type tensor (i.e. a tensor satisfying the properties of the curvature tensor of the Levi-Civita connection in the special class of the parallel structures on the manifold) is determined. The associated 1-forms are derived by the scalar curvatures of the K\"ahler-type tensor for the canonical connection on the manifolds from the main classes with closed 1-forms.

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