摘要 : We study the equations governing rigid \( \mathcal{N}=1 \) supersymmetry in five dimensions. If the supersymmetry spinor satisfies a reality condition, these are foliations admitting families of almost complex structures on the le... 展开 We study the equations governing rigid \( \mathcal{N}=1 \) supersymmetry in five dimensions. If the supersymmetry spinor satisfies a reality condition, these are foliations admitting families of almost complex structures on the leaves. In other words, all these manifolds have families of almost Cauchy-Riemann (CR) structures. After deriving integrability conditions under which circumstances the almost CR structure defines a CR manifold or a transversally holomorphic foliation (THF), we discuss implications on localization. We also discuss potential global obstructions to the existence of solutions 收起