标题： 电荷、复结构和瞬子的扰动 显示英文标题

标题： Charges, complex structures, and perturbations of instantons

摘要： 具有通过Killing旋量进行自旋降低的准局部守恒电荷的Hermitian非-Kähler Einstein 4流形，对应于模空间的一个参数。 该电荷已对所有显式已知的例子进行了计算。 展示了无穷小Einstein变形可以接受一个闭合的2-形式，该形式衡量对该电荷的扰动。 在满足某些边界条件的情况下，显示穿过Hermitian非-Kähler Einstein度量的模空间中的度量曲线在二阶微扰顺序下是共形Kähler的。 该结果被用于证明ALF Hermitian非-Kähler瞬子的无穷小Ricci平坦变形与Hermitian瞬子的模空间相切，因此作为结果，无穷小刚性成立。 该陈述的类似情况也适用于紧致Hermitian非-Kähler Einstein度量的情况。 显示英文摘要

摘要： Hermitian non-K\"ahler Einstein 4-manifolds have a quasi-locally conserved charge associated to spin-lowering via Killing spinors, and corresponding to a parameter of the moduli space. This charge is evaluated for all explicitly known examples. Infinitesimal Einstein deformations are shown to admit a closed 2-form that measures the perturbation to this charge. Provided certain boundary conditions hold, a curve of metrics in the moduli space passing through a Hermitian non-K\"ahler Einstein metric is shown to be conformally K\"ahler to second perturbative order. This result is applied to prove that infinitesimal Ricci-flat deformations of ALF Hermitian non-K\"ahler instantons are tangent to the moduli space of Hermitian instantons, and hence as a consequence that infinitesimal rigidity holds. The analog of this statement also holds for the case of compact Hermitian non-K\"ahler Einstein metrics.