Tohoku Mathematical Journal

On the curvature of the Fefferman metric of contact Riemannian manifolds

Masayoshi Nagase

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 18 September 2019

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

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

Fefferman metric scalar curvature contact Riemannian structure hermitian Tanno connection


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.

Export citation


  • E. Barletta and S. Dragomir, Differential equations on contact Riemannian manifolds, Ann. Scuola Norm. Sup. Pisa, Cl. Sci. (4) 30 (1) (2001), 63–95.
  • D. E. Blair and S. Dragomir, Pseudohermitian geometry on contact Riemannian manifolds, Rend. Mat. Appl. (7) 22 (2002), 275–341.
  • S. Dragomir and G. Tomassini, Differential geometry and analysis on CR manifolds, Progress in Math. 246, Birkhäuser, Boston-Basel-Berlin, 2006.
  • C. Fefferman, Monge-Ampère equations, the Bergman kernel, and geometry of pseudoconvex domains, Ann. of Math. 103 (1976), 395–416 104 (1976), 393–394.
  • R. Imai and M. Nagase, The second term in the asymptotics of Kohn-Rossi heat kernel on contact Riemannian manifolds, preprint.
  • J. M. Lee, The Fefferman metric and pseudohermitian invariants, Trans. Amer. Math. Soc. 296 (1) (1986), 411–429.
  • M. Nagase, The heat equation for the Kohn-Rossi Laplacian on contact Riemannian manifolds, preprint.
  • M. Nagase, CR conformal Laplacian and some invariants on contact Riemannian manifolds, preprint.
  • M. Nagase and D. Sasaki, Hermitian Tanno connection and Bochner type curvature tensors of contact Riemannian manifolds, J. Math. Sci. Univ. Tokyo 25(2018), 149–169.
  • S. Tanno, Variational problems on contact Riemannian manifolds, Trans. Amer. Math. Soc. 314 (1) (1989), 349–379.