四维天体方程的伙伴对称与非不变解
Partner symmetries and non-invariant solutions of four-dimensional heavenly equations
摘要：
我们将我们的伙伴对称性方法推广到双曲复Monge-Ampère方程和第二天堂Plebañski方程。我们证明了这两个方程的伙伴对称性的存在，并推导出它们之间的关系。对于某些简单的选择合作伙伴的对称性所产生的微分约束连同原来的天堂方程被转化为线性方程组的适当的勒让德变换。这些线性方程的解一般是非不变的。因此，我们得到明确的新类的天堂度量没有杀死向量。
英文摘要：
We extend our method of partner symmetries to the hyperbolic complex Monge-Ampère equation and the second heavenly equation of Plebañski. We show the existence of partner symmetries and derive the relations between them for both equations. For certain simple choices of partner symmetries the resulting differential constraints together with the original heavenly equations are transformed to systems of linear equations by an appropriate Legendre transformation. The solutions of these linear equations are generically non-invariant. As a consequence we obtain explicitly new classes of heavenly metrics without Killing vectors.
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