  We study the equations governing rigid 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.
