三维到四维天体方程非不变解的提升和新的超双曲度规
Lift of noninvariant solutions of heavenly equations from three to four dimensions and new ultra-hyperbolic metrics
摘要：
我们证明了伙伴对称提供了三维Boyer-Finley方程的非不变解到四维双曲复Monge-Ampere方程的非不变解的提升.升降机适用于非不变的解决方案的Boyer-Finley方程，获得较早的方法组叶状，产生非不变的解决方案的双曲型复杂的蒙赫-安培方程。利用这些解，我们构造了新的具有非零曲率张量且不含Killing向量的Ricci平坦超双曲度量。
英文摘要：
We demonstrate that partner symmetries provide a lift of noninvariant solutions of three-dimensional Boyer-Finley equation to noninvariant solutions of four-dimensional hyperbolic complex Monge-Ampere equation. The lift is applied to noninvariant solutions of the Boyer-Finley equation, obtained earlier by the method of group foliation, to yield noninvariant solutions of the hyperbolic complex Monge-Ampere equation. Using these solutions we construct new Ricci-flat ultra-hyperbolic metrics with non-zero curvature tensor that have no Killing vectors.
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