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

TL;DR

This paper introduces a new class of manifolds with almost contact 3-structure combining different metric types, and explores their properties and examples, linking them to almost hypercomplex manifolds with Hermitian-Norden metrics.

Contribution

It defines manifolds with almost contact 3-structure involving mixed metric types and studies their properties and examples, expanding the understanding of such geometric structures.

Findings

Manifolds of cosymplectic type are characterized.

Product with real line yields almost hypercomplex manifolds.

Examples illustrate the theoretical constructions.

Abstract

It is introduced a differentiable manifold with almost contact 3-structure which consists of an almost contact metric structure and two almost contact B-metric structures. The product of this manifold and a real line is an almost hypercomplex manifold with Hermitian-Norden metrics. It is proven that the introduced manifold of cosymplectic type is at. Some examples of the studied manifolds are given.