The Complex Vacuum Metric with Minimally Degenerated Conformal Curvature
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.
KeywordsStructural Function Einstein Equation Curvature Form Einstein Vacuum Equation Degenerate Solution
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