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Harmonic Vector Fields on Pseudo-Riemannian Manifolds

Friswell, Robert Michael (2014) Harmonic Vector Fields on Pseudo-Riemannian Manifolds. PhD thesis, University of York.

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Abstract

This thesis generalises the theory of harmonic vector fields to the non-compact pseudo- Riemannian case. After introducing the required background theory we consider the first variation of the local energies to find the Euler-Lagrange equations for this new case. We then introduce a natural closed conformal gradient field on pseudo-Riemannian warped products and find the Euler-Lagrange equations for harmonic closed conformal vector fields of this sort. We then give examples of such harmonic closed conformal fields, this leads to a harmonic vector fields on a 2-sphere with a rotationally symmetric singular metric. The harmonic conformal gradient fields on all hyperquadrics are then categorised up to con- gruence. The harmonic Killing fields on the 2-dimensional hyperquadrics are found, and shown to be unique up to congruence.

Item Type: Thesis (PhD)
Academic Units: The University of York > Mathematics (York)
Identification Number/EthosID: uk.bl.ethos.634382
Depositing User: Mr Robert Michael Friswell
Date Deposited: 03 Feb 2015 12:54
Last Modified: 08 Sep 2016 13:32
URI: http://etheses.whiterose.ac.uk/id/eprint/7878

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