Some constructions of almost para-hyperhermitian structures on manifolds and tangent bundles

TL;DR

This paper constructs examples of almost para-hyperhermitian structures on various manifolds, including tangent bundles and product manifolds, expanding the understanding of such geometric structures.

Contribution

It provides new explicit constructions of almost para-hyperhermitian structures on tangent bundles and product manifolds with mixed 3-structures.

Findings

Examples of almost para-hyperhermitian structures on tangent bundles

Construction on product manifolds with mixed 3-structures

Structures on circle bundles over manifolds with mixed 3-structures

Abstract

In this paper we give some examples of almost para-hyperhermitian structures on the tangent bundle of an almost product manifold, on the product manifold $M\times\mathbb{R}$, where $M$ is a manifold endowed with a mixed 3-structure and on the circle bundle over a manifold with a mixed 3-structure.