Use this URL to cite or link to this record in EThOS:
Title: Harmonic vector fields on pseudo-Riemannian manifolds
Author: Friswell, Robert Michael
ISNI:       0000 0004 5350 857X
Awarding Body: University of York
Current Institution: University of York
Date of Award: 2014
Availability of Full Text:
Access from EThOS:
Access from Institution:
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.
Supervisor: Wood, Chris M. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available