Examples of 3-quasi-Sasakian manifolds

TL;DR

This paper introduces a general method for constructing quasi-Sasakian 3-structures on high-dimensional manifolds and presents the first explicit example of a compact 3-quasi-Sasakian manifold that is not a simple product of known special manifolds.

Contribution

It provides a new construction technique for quasi-Sasakian 3-structures and offers the first explicit non-product example of a compact 3-quasi-Sasakian manifold.

Findings

General construction method for quasi-Sasakian 3-structures

First explicit non-product compact 3-quasi-Sasakian manifold

New insights into manifold structures with special geometric properties

Abstract

We provide a general method to construct examples of quasi-Sasakian 3-structures on a (4n+3)-dimensional manifold. Moreover, among this class, we give the first explicit example of a compact 3-quasi-Sasakian manifold which is not the global product of a 3-Sasakian manifold and a hyper-K\"ahler manifold.