An involutive diffeomorphism σ of a connected smooth manifold M is called dissecting if the complement of its fixed point set is not connected. Dissecting involutions on a complete Riemannian manifold are closely related to constructive quantum field theory through the work of Dimock and Jaffe/Ritter on the construction of reflection positive Hilbert spaces. In this article we classify all pairs (M, σ), where M is an irreducible connected symmetric space, not necessarily Riemannian, and σ is a dissecting involutive automorphism. In particular, we show that the only irreducible, connected and simply connected Riemannian symmetric spaces with dissecting isometric involutions are \( {\mathbbm{S}}^n \) and ℍⁿ, where the corresponding fixed point spaces are \( {\mathbbm{S}}^{n-1} \) and ℍ^n − 1, respectively.

如果未连接其光滑定点集的补集，则将连接的光滑歧管M的对合微分σ称为解剖。通过Dimock和Jaffe / Ritter在构造正反射希尔伯特空间上的工作，在完整的黎曼流形上剖析对合与构造性量子场理论密切相关。在本文中，我们对所有对（M， σ）进行分类，其中M是不可约的连接对称空间，不一定是黎曼方程，而σ是解剖的对合自同构。特别是，我们证明了唯一的不可约，连通和简单连通的带有等距对合的黎曼对称空间是\（{\ mathbbm {S}} ^ N \）和ℍ ^Ñ，其中相应的固定点空间是\（{\ mathbbm {S}} ^ {N - 1} \）和ℍ ^{ñ  - 1}，分别。