On Local Characterization Results in Geometry and Gravitation

Marc Mars ()
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Marc Mars: Instituto de Física Fundamental y Matemáticas, IUFFyM, Universidad de Salamanca

A chapter in From Riemann to Differential Geometry and Relativity, 2017, pp 541-570 from Springer

Abstract: Abstract An important problem in differential geometry and in gravitation is to identify metrics in a fully coordinate independent manner. In fact, the very foundation of Riemannian geometry is based on the existence of a tensor, the Riemann or curvature tensor, which vanishes if and only if the metric is locally flat. Many other such local characterizations of metrics are known. The aim of this article is to present a brief selection of them as an example of the fruitful interplay between differential geometry and gravity.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-60039-0_18

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DOI: 10.1007/978-3-319-60039-0_18

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