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

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

2007-06-06

arxiv.org/abs/0706.0888v3

Mathematics

Differential Geometry

To appear on Rocky Mountain J. Math

Scientific paper

We find necessary and sufficient conditions for the bi-Legendrian connection $\nabla$ associated to a bi-Legendrian structure $(\cal F,\cal G)$ 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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