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- W1985802214 abstract "The Poincaré group is well known to imply a deep connection between the structure of space-time and particle properties. Searching for the analogous mathematical structure for curved space-time, we investigate the role of 10-parametric classes of coordinate systems in curved space-times. It is shown that all coordinate systems can be divided into 10-parametric classes according to the values of gμν and certain nontensorial combinations of its derivatives to an arbitrarily high order at a given point. It is also shown that 10-parametric classes arise naturally in Riemannian space-time when the maximum freedom in assigning numerical values to such nontensorial quantities is used. The set of transformations between members of a given class does not form a group, in general, but a novel mathematical structure (a ``quasigroup''). New results concerning the transformations between normal coordinates and the analytic characterization of geodesic Fermi coordinates are derived." @default.
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- W1985802214 date "1971-02-01" @default.
- W1985802214 modified "2023-10-17" @default.
- W1985802214 title "Quasigroups of Coordinate Transformations in Curved Space-Time" @default.
- W1985802214 cites W1989102461 @default.
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- W1985802214 doi "https://doi.org/10.1063/1.1665579" @default.
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