复Monge-Ampere方程的伙伴对称性产生不连续对称性的超Kahler度量
Partner symmetries of the complex Monge-Ampere equation yield hyper-Kahler metrics without continuous symmetries
摘要：
我们将Mason-Newman拉克斯对推广到椭圆型复Monge-Ampère方程，使该方程本身成为一个代数结果.我们把推广的Lax方程中的函数看作是一个复势。我们确定的实部和虚部的潜力，我们称之为伙伴对称性，分别与平移和平移对称性的特点。然后，我们选择对称性特征作为新的未知量来代替Kähler势，直接导致Legendre变换和一组由单个实势满足的线性方程组。这使得我们能够构造复Monge-Ampère方程的Legendre变换的非不变解，并获得具有反自对偶Riemann曲率2-形式的不允许Killing向量的超Kähler度量。
英文摘要：
We extend the Mason-Newman Lax pair for the elliptic complex Monge-Ampère equation so that this equation itself emerges as an algebraic consequence. We regard the function in the extended Lax equations as a complex potential. We identify the real and imaginary parts of the potential, which we call partner symmetries, with the translational and dilatational symmetry characteristics respectively. Then we choose the dilatational symmetry characteristic as the new unknown replacing the Kähler potential which directly leads to a Legendre transformation and to a set of linear equations satisfied by a single real potential. This enables us to construct non-invariant solutions of the Legendre transform of the complex Monge-Ampère equation and obtain hyper-Kähler metrics with anti-self-dual Riemann curvature 2-form that admit no Killing vectors.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
