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On the Fefferman class of metrics associated with a three-dimensional CR space

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Abstract

We derive the explicit forms of Fefferman's metric for a Cauchy-Riemann space admitting a solution of the tangential Cauchy-Riemann equation and of the corresponding Weyl tensor. We show that its Petrov type is 0 in the case of the hyperquadric or N in all other cases, and that the Fefferman class of metrics does not contain any nonflat solution of Einstein's vacuum equations with cosmological constant.

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Authors and Affiliations

  1. Institute of Theoretical Physics, Warsaw University, Hoza 69, 00-691, Warsaw, Poland

    Jerzy Lewandowski

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  1. Jerzy Lewandowski
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Work supported in part by the Polish Ministry of Science and Higher Education, Research Problem CPBP 01.03.

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Lewandowski, J. On the Fefferman class of metrics associated with a three-dimensional CR space. Letters in Mathematical Physics 15, 129–135 (1988). https://doi.org/10.1007/BF00397833

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  • DOI: https://doi.org/10.1007/BF00397833

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