Tohoku Mathematical Journal

On the curvature of the Fefferman metric of contact Riemannian manifolds

Masayoshi Nagase

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Abstract

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.

Article information

Source
Tohoku Math. J. (2), Volume 71, Number 3 (2019), 425-436.

Dates
First available in Project Euclid: 18 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1568772179

Digital Object Identifier
doi:10.2748/tmj/1568772179

Mathematical Reviews number (MathSciNet)
MR4012356

Subjects
Primary: 53B30: Lorentz metrics, indefinite metrics
Secondary: 53D15: Almost contact and almost symplectic manifolds

Keywords
Fefferman metric scalar curvature contact Riemannian structure hermitian Tanno connection

Citation

Nagase, Masayoshi. On the curvature of the Fefferman metric of contact Riemannian manifolds. Tohoku Math. J. (2) 71 (2019), no. 3, 425--436. doi:10.2748/tmj/1568772179. https://projecteuclid.org/euclid.tmj/1568772179


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References

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