The Complex Vacuum Metric with Minimally Degenerated Conformal Curvature

  • Jerzy F. Plebanski
  • Ivor Robinson


By applying Plebański-Hacyan theorem, the canonical forms of the metric are established for all complex Einstein flat with the minimally (one-sided) algebraically degenerate — conformal curvature. Then Einstein equations are integrated. The solution is expressed in the terms of only one fundamental key function which is determined by a differential equation of the second order and with quadratic non-linearity only, this equation being a generalization of the second heavenly equation.


Structural Function Einstein Equation Curvature Form Einstein Vacuum Equation Degenerate Solution 
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Copyright information

© Plenum Press, New York 1977

Authors and Affiliations

  • Jerzy F. Plebanski
    • 1
    • 2
  • Ivor Robinson
    • 3
  1. 1.Centro de Investigacion y Estudios Avanzados 14-740D.F. MexicoMexico
  2. 2.University of WarsawWarsawPoland
  3. 3.Institute for Mathematical SciencesThe University of Texas at DallasRichardsonUSA

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