Almost formality of quasi-Sasakian and Vaisman manifolds with applications to nilmanifolds

TL;DR

This paper investigates the near-formality of certain compact manifolds with transversely Kaehler structures, specifically Vaisman and quasi-Sasakian manifolds, and applies these findings to classify related nilmanifolds.

Contribution

It introduces models that approximate formality for these manifolds and uses them to classify associated nilmanifolds.

Findings

Models close to being formal for Vaisman and quasi-Sasakian manifolds

Classification of nilmanifolds admitting these structures

Extension of formality concepts to specific geometric structures

Abstract

We provide models that are as close as possible to being formal for a large class of compact manifolds that admit a transversely Kaehler structure, including Vaisman and quasi-Sasakian manifolds. As an application we are able to classify the corresponding nilmanifolds.