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On the curvature of the Fefferman metric of contact Riemannian manifolds. (English) Zbl 1431.53087
Summary: It is known that a contact Riemannian manifold carries a generalized Fefferman metric on a circle bundle over the manifold. We compute the curvature of the metric explicitly in terms of a modified Tanno connection on the underlying manifold. In particular, we show that the scalar curvature descends to the pseudohermitian scalar curvature multiplied by a certain constant. This is an answer to a problem considered by Blair-Dragomir.

MSC:
53D10 Contact manifolds (general theory)
53D15 Almost contact and almost symplectic manifolds
53B20 Local Riemannian geometry
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References:
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