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

TL;DR

This paper investigates the conditions under which higher-dimensional generalizations of normal almost contact structures, called f.pk-structures, are normal on g-manifolds, revealing that normality is restricted to abelian Lie algebras.

Contribution

It introduces and analyzes f.pk-structures on g-manifolds, establishing that normality conditions are satisfied only when the Lie algebra g is abelian or 3-dimensional with specific constructions.

Findings

Normality only when g is abelian in the first case.

Constructs almost complex structures on product manifolds.

Normality conditions depend on structure tensors.

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.