On a Grassmann odd analogue of Carrollian Manifolds

We define a Grassmann odd analogue of a Carrollian manifold as a supermanifold of dimension $n\mathrm{\mid }1$ with an even degenerate metric such that the kernel is generated by a non-singular odd vector field that is a supersymmetry generator. Alongside other results, we establish that the reduced manifold is a pseudo-Riemannian manifold, and show that compatible affine connections always exist, albeit they must carry torsion. As a physically relevant example, we examine an Inönü–Wigner contraction of the supertranslation algebra on standard superspace ${\mathbb{R}}^{4\mathrm{\mid }4}$.