×

zbMATH — the first resource for mathematics

On the degrees of freedom of a semi-Riemannian metric. (English) Zbl 1069.53056
The authors show that any analytic semi-Riemannian metric can be obtained as a deformation of a constant curvature metric, and the deformation can be parametrized by an analytic 2-form.
The proof is by induction over the dimension \(n\), starting with the trivial case \(n=1\). Also the Cauchy problem has to be used for the proof.
Applications are given especially for the 4-dimensional case.
The present paper generalizes earlier results of the authors to the case of arbitrary dimension of space-time.
By the way, Ref. [1] of the paper, G. F. B. Riemann, from 1959, is the English translation of the German language Habilitation from Bernhard Riemann entitled “Über die Hypothesen, welche der Geometrie zu Grunde liegen”, from 1854.

MSC:
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
83E05 Geometrodynamics and the holographic principle
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
PDF BibTeX XML Cite
Full Text: DOI