Homogeneous Nonrelativistic Geometries as Coset Spaces

Understand

We generalize the coset procedure of homogeneous spacetimes in (pseudo-)Riemannian geometry to non-Lorentzian geometries.

• These are manifolds endowed with nowhere vanishing invertible vielbeins that transform under local non-Lorentzian tangent space transformations.
• In particular, we focus on nonrelativistic symmetry algebras that give rise to (torsional) Newton-Cartan geometries, for which we demonstrate how the Newton-Cartan metric complex is determined by degenerate co- and contravariant symmetric bilinear forms on the coset.
• In specific cases, we also show the connection of the resulting nonrelativistic coset spacetimes to pseudo-Riemannian cosets via In\"on\"u-Wigner contraction of relativistic algebras as well as null reduction.