Generalized Newton–Cartan geometries for particles and strings

Abstract We discuss the generalized Newton–Cartan geometries that can serve as gravitational background fields for particles and strings. In order to enable us define affine connections are invariant under all symmetries of structure group, we describe torsionful with independent torsion tensors. A characteristic feature non-Lorentzian consider is some tensors so-called ‘intrinsic torsion’ Setting components these intrinsic zero leads constraints on geometry. For both strings, various such be imposed consistently group symmetries. this way, reproduce several results in literature.