Leibnizian , Galilean and Newtonian structures of space – timea ...
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چکیده
The following three geometrical structures on a manifold are studied in detail: Leibnizian: a nonvanishing one-form V 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 1 ~gauge field! which parallelizes V and ^•,•&. For any fixed vector field of observers Z(V(Z)[1), an explicit Koszul-type formula which reconstructs bijectively all the possible 1’s from the gravitational Ga1ZZ and vorticity va 1 2 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 v[0!. Classical concepts in Newtonian theory are revisited and discussed. © 2003 American Institute of Physics. @DOI: 10.1063/1.1541120#
منابع مشابه
Leibnizian, Galilean and Newtonian structures of spacetime
The following three geometrical structures on a manifold are studied in detail: Leibnizian: a non-vanishing 1-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 a...
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تاریخ انتشار 2003