We find necessary and sufficient conditions for the bi-Legendrian connection \nabla associated to a bi-Legendrian structure (F,G) on a contact metric manifold (M,\phi,\xi,\eta,g) being a metric connection and then we give conditions ensuring that \nabla coincides with the (generalized) Tanaka-Webster connection of (M,\phi,\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.

### 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 (F,G) on a contact metric manifold (M,\phi,\xi,\eta,g) being a metric connection and then we give conditions ensuring that \nabla coincides with the (generalized) Tanaka-Webster connection of (M,\phi,\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.
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2010
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/16461
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