Leibnizian, Galilean and Newtonian structures of space–time Available to Purchase

The following three geometrical structures on a manifold are studied in detail: Leibnizian: a nonvanishing one-form Ω plus a Riemannian metric 〈⋅,⋅〉 on its annhilator vector bundle. In particular, the possible dimensions of the automorphism group of a Leibnizian $G$-structure are characterized. Galilean: Leibnizian structure endowed with an affine connection ∇ (gauge field) which parallelizes Ω and 〈⋅,⋅〉. For any fixed vector field of observers $Z(Ω(Z)≡1),$ an explicit Koszul-type formula which reconstructs bijectively all the possible ∇’s from the gravitational $G≔∇ZZ$ and vorticity ω≔$12$ rot $Z$ fields (plus eventually the torsion) is provided. Newtonian: Galilean structure with 〈⋅,⋅〉 flat and a field of observers $Z$ which is inertial (its flow preserves the Leibnizian structure and ω≡0). Classical concepts in Newtonian theory are revisited and discussed.