On normality of f.pk-structures on g-manifolds

2016/09/27 by Czarnecki, Andrzej, Sroka, Marcin, Wolak, Robert
#53C12 #53C15 #53C25 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1609.08601

Abstract

We consider higher dimensional generalisations of normal almost contact structures, the so called f.pk-structures where parallelism spans a Lie algebra g (f.pk-g-structures). Two types of these structures are discussed. In the first case, we construct an almost complex structure on a product manifold mirroring K-structures. We show that the natural normality condition can be satisfied only when g is abelian. The second case we consider is when the Lie algebra in question is 3-dimensional, but the almost complex structure on a product is constructed in a different manner. In both cases the normality conditions are expressed in terms of the structure tensors.

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