标题： 施瓦茨-斯托克斯方程和S4上的SU2不变瞬子 显示英文标题

标题： Isomonodromic deformations and SU2-invariant instantons on S4

摘要： 反自对偶（ASD）的杨-米尔斯方程解（或瞬子）在反自对偶四维流形上，当在三维李群的适当作用下保持不变时，通过扭子构造会生成在C P 1上具有四个简单奇点的联络的同单值变形。 众所周知，这种变形由第六个皮亚诺方程P vi（{\alpha }，\b{eta}，{\gamma }，{\delta }）来控制。 我们研究SU 2在S 4上的特殊情况，该情况来源于R 5上的不可约表示。 特别是，我们将参数 ({\alpha }, \b{eta}, {\gamma }, {\delta }) 用瞬子数来表示。 本文包含了对[16]中宣布的结果的证明。 显示英文摘要

摘要： Anti-self-dual (ASD) solutions to the Yang-Mills equation (or instantons) over an anti-self-dual four manifold, which are invariant under an appropriate action of a three dimensional Lie group, give rise, via twistor construction, to isomonodromic deformations of connections on C P 1 having four simple singularities. As is well known this kind of deformations is governed by the sixth Painlev\'e equation P vi ({\alpha}, \b{eta}, {\gamma}, {\delta}) . We work out the particular case of the SU 2 -action on S 4 , obtained from the irreducible representation on R 5 . In particular, we express the pa- rameters ({\alpha}, \b{eta}, {\gamma}, {\delta}) in terms of the instanton number. The present paper contains the proof of the result anounced in [16].