We establish several relationships between the non-relativistic conformal symmetries of Newton–Cartan geometry and the Schrödinger equation. In particular we discuss the algebra sch(d) of vector fields conformally-preserving ...

We develop a non-relativistic twistor theory, in which Newton-Cartan structures of Newtonian gravity correspond to complex three-manifolds with a four-parameter family of rational curves with normal bundle O ⊕ O(2). We ...