Tohoku Mathematical Journal
2019
September
SECOND SERIES VOL. 71, NO. 3

Tohoku Math. J.
71 (2019), 425-436

Title ON THE CURVATURE OF THE FEFFERMAN METRIC OF CONTACT RIEMANNIAN MANIFOLDS

Author Masayoshi Nagase

(Received February 15, 2017, revised June 26, 2017)
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.

Mathematics Subject Classification. Primary 53B30; Secondary 53D15.
Key words and phrases. Fefferman metric, scalar curvature, contact Riemannian structure, hermitian Tanno connection.

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