Degenerate Spin Structures and the Levy-Leblond Equation
  Newton-Cartan manifolds and the Galilei group are defined by the use of co-rank one degenerate metric tensor. Newton-Cartan connection is lifted to the degenerate spinor bundle over a Newton-Cartan 4-manifold by the aid of degenerate spin group. Levy-Leblond equation is constructed with the lifted connection. 
T. Dereli, S. Kocak, M. Limoncu