On generalized quasi-Sasaki manifolds

TL;DR

This paper explores a broader class of 5-dimensional almost contact metric manifolds, generalizing quasi-Sasaki structures, characterizing their intrinsic torsion, and providing new examples beyond the classical quasi-Sasaki case.

Contribution

It introduces a generalized class of quasi-Sasaki manifolds, characterizes their intrinsic torsion, and constructs explicit examples that are not quasi-Sasaki.

Findings

Existence of a unique metric connection compatible with the structure

Characterization of these manifolds by their intrinsic torsion

Construction of non-quasi-Sasaki examples

Abstract

We study 5-dimensional Riemannian manifolds that admit an almost contact metric structure. In particular, we generalize the class of quasi-Sasaki manifolds and characterize these structures by their intrinsic torsion. Among other things, we see that these manifolds admit a unique metric connection that is compatible with the underlying almost contact metric structure. Finally, we construct a family of examples that are not quasi-Sasaki.