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

Abstract

We find necessary and sufficient conditions for the bi-Legendrian connection $\nabla$ associated to a bi-Legendrian structure $(\mathcal{F},\mathcal{G})$ on a contact metric manifold $(M,\varphi ,\xi ,\eta ,g)$ being a metric connection and then we give conditions ensuring that $\nabla$ coincides with the (generalized) Tanaka-Webster connection of $(M,\varphi ,\xi ,\eta ,g)$. Using these results, we give some interpretations of the Tanaka-Webster connection and we study the interactions between the Tanaka-Webster, the bi-Legendrian and the Levi Civita connection in a Sasakian manifold.

arXiv commentTo appear on Rocky Mountain J. Math

References in corpus (1)

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

Cited by in corpus (4)

• Nullity conditions in paracontact geometry
• Sasaki-Einstein and paraSasaki-Einstein metrics from (κ,μ)-structures
• Contact metric $(\kappa ,\mu )$-spaces as bi-Legendrian manifolds
• $N(\kappa )-$contact Metric Manifolds with Generalized Tanaka-Webster Connection