2025/08/19 by Andrew James Bruce, Bruce, Andrew James
Mathematics · #53B05 #58A50 #58C50 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Physics (math-ph) #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2508.14240
openalex publication_date 2025/08/19 · openalex created_date 2025/10/16 · openalex updated_date 2026/08/01
We define a Grassmann odd analogue of a Carrollian manifold as a supermanifold of dimension n|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 ℝ4|4.