A NOTE ON WEAK H-SPACES HEAVENLY EQUATIONS AND THEIR EVOLUTION WEAK HEAVENLY EQUATIONS

摘要

Using the weak heavens condition we find a non-linear partial differential equation which is shown to generalize the heavenly equation of Self-dual gravity. This differential equation we call "weak heavenly equation" (WH-equation). For the two-dimensional case the WH-equation is brought into the evolution (Cauchy-Kovalevski) form using a Legendre transformation. Finally, we find that this transformed equation ("evolution weak heavenly equation") does admit very simple solutions.