Contact metric $(\kappa,\mu)$-spaces as bi-Legendrian manifolds

TL;DR

This paper explores contact metric $(ppa,mu)$-spaces by viewing them as bi-Legendrian manifolds and characterizing their structure through a canonical connection.

Contribution

It introduces a new perspective by relating contact metric $(ppa,mu)$-spaces to bi-Legendrian manifolds and defines a canonical connection for these spaces.

Findings

Characterization of contact metric $(ppa,mu)$-spaces via bi-Legendrian structures

Definition of a canonical connection on these spaces

Insight into the geometric structure of $(ppa,mu)$-spaces

Abstract

We regard a contact metric manifold whose Reeb vector field belongs to the $(\kappa,\mu)$-nullity distribution as a bi-Legendrian manifold and we study its canonical bi-Legendrian structure. Then we characterize contact metric $(\kappa,\mu)$-spaces in terms of a canonical connection which can be naturally defined on them.