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Conformal Einstein spaces

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Abstract

We study conformal transformations in four-dimensional manifolds. In particular, we present a new set of two necessary and sufficient conditions for a space to be conformal to an Einstein space. The first condition defines the class of spaces conformal to C spaces, whereas the last one (the vanishing of the Bach tensor) gives the particular subclass ofC spaces which are conformally related to Einstein spaces.

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of Pittsburgh, 15260, Pittsburgh, Pennsylvania

    Carlos N. Kozameh & Ezra T. Newman

  2. Mathematical Institute, Oxford University, Oxford, England

    K. P. Tod (S.E.R.C. Advanced Fellow)

Authors
  1. Carlos N. Kozameh
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  2. Ezra T. Newman
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  3. K. P. Tod
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Additional information

This work has been partly supported bym a grand from the National Science Foundation.

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Kozameh, C.N., Newman, E.T. & Tod, K.P. Conformal Einstein spaces. Gen Relat Gravit 17, 343–352 (1985). https://doi.org/10.1007/BF00759678

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  • DOI: https://doi.org/10.1007/BF00759678

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