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

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.

To appear on Bull. Austral. Math. Soc

References in corpus (1)

• Some remarks on the generalized Tanaka-Webster connection of a contact metric manifold

Cited by in corpus (3)

• Nullity conditions in paracontact geometry
• Sasaki-Einstein and paraSasaki-Einstein metrics from (κ,μ)-structures
• Some remarks on the generalized Tanaka-Webster connection of a contact metric manifold