An instanton (E, D) on a (pseudo-)hyperkähler manifold M is a vector bundle E associated with a principal G-bundle with a connection D whose curvature is pointwise invariant under the quaternionic structures of \(T_x M,~x\in M\), and thus satisfies the Yang–Mills equations. Revisiting a construction of solutions, we prove a local bijection between gauge equivalence classes of instantons on M and equivalence classes of certain holomorphic functions taking values in the Lie algebra of \(G^{\mathbb {C}}\) defined on an appropriate \(\mathrm {SL}_2({\mathbb {C}})\)-bundle over M. Our reformulation affords a streamlined proof of Uhlenbeck’s compactness theorem for instantons on (pseudo-)hyperkähler manifolds.

（伪）Hyperkähler流形M上的一个瞬时子（E，  D）是与主G-束相关联的向量束E，该主束具有连接D，其曲率在\（T_x M，〜x \以M \） ，因此满足杨-米尔斯方程。回顾解决方案的构造，我们证明了M上的标量的等价等价类与某些全纯函数的等价类之间的局部双射，并采用了在适当的条件下定义的\（G ^ {\ mathbb {C}} \\ \（\ mathrm {SL} _2（{\ mathbb {C}}）\） -捆绑中号。我们的重构为（伪）Hyperkähler流形上的瞬时子提供了Uhlenbeck紧性定理的简化证明。