Proof of a decomposition theorem for symmetric tensors on spaces with constant curvature
| dc.creator | Straumann, Norbert | |
| dc.date | 2008-05-29 | |
| dc.date.accessioned | 2026-07-07T12:20:03Z | |
| dc.date.available | 2026-07-07T12:20:03Z | |
| dc.description | In cosmological perturbation theory a first major step consists in the decomposition of the various perturbation amplitudes into scalar, vector and tensor perturbations, which mutually decouple. In performing this decomposition one uses -- beside the Hodge decomposition for one-forms -- an analogous decomposition of symmetric tensor fields of second rank on Riemannian manifolds with constant curvature. While the uniqueness of such a decomposition follows from Gauss' theorem, a rigorous existence proof is not obvious. In this note we establish this for smooth tensor fields, by making use of some important results for linear elliptic differential equations. | |
| dc.description | 4 pages, accepted for publication in Annalen der Physik | |
| dc.identifier | https://arxiv.org/abs/0805.4500 | |
| dc.identifier | http://arxiv.org/abs/0805.4500 | |
| dc.identifier | Annalen Phys.17:609-611,1997 | |
| dc.identifier | doi:10.1002/andp.200810312 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/212965 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | Proof of a decomposition theorem for symmetric tensors on spaces with constant curvature | |
| dc.type | text |