We study invariant systems of PDEs defining Killing vector-valued forms, and then we specialize to Killing spinor-valued forms. We give a detailed treatment of their prolongation and integrability conditions by relating the point-wise values of solutions to the curvature of the underlying manifold. As an example, we completely solve the equations on model spaces of constant curvature producing brand new solutions which do not come from the tensor product of Killing spinors and Killing-Yano forms.

中文翻译：

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杀死自旋值形式及其可积性条件

我们研究了定义 Killing 向量值形式的 PDE 不变系统，然后我们专门研究了 Killing 自旋值形式。我们通过将解的逐点值与底层流形的曲率相关联，详细处理了它们的延展性和可积性条件。举个例子，我们完全求解常曲率模型空间上的方程，产生全新的解，这些解不是来自 Killing spinors 和 Killing-Yano 形式的张量积。