 203 L. T. Stepien
 On some exact solutions of heavenly equations in four dimensions
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Jan 14, 20

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Abstract. Some new classes of exact solutions (socalled functionallyinvariant solutions) of the elliptic and hyperbolic complex MongeAmp$\grave{e}$re equations and of the second heavenly equation, mixed heavenly equation, asymmetric heavenly equation, evolution form of second heavenly equation, general heavenly equation, real general heavenly equation and one of the real sections of general heavenly equation, are found. Besides noninvariance of these found classes of solutions has been investigated. These classes of solutions determine the new classes of metrics without Killing vectors. A criterion of noninvariance of the solutions belonging to found classes, has been also formulated.
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