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dc.contributor.advisorFigueroa-O'Farrill, Jose
dc.contributor.advisorAlekseevskii, Dmitri
dc.contributor.authorReynolds, Paul
dc.date.accessioned2012-08-07T14:15:02Z
dc.date.available2012-08-07T14:15:02Z
dc.date.issued2012-06-25
dc.identifier.urihttp://hdl.handle.net/1842/6218
dc.description.abstractThis thesis comes in three main parts. In the first of these (comprising chapters 2 - 6), the basic theory of Riemannian and conformal submersions is described and the relevant geometric machinery explained. The necessary Clifford algebra is established and applied to understand the relationship between the spinor bundles of the base, the fibres and the total space of a submersion. O'Neill-type formulae relating the covariant derivatives of spinor fields on the base and fibres to the corresponding spinor field on the total space are derived. From these, formulae for the Dirac operators are obtained and applied to prove results on Dirac morphisms in cases so far unpublished. The second part (comprising chapters 7-9) contains the basic theory and known classifications of G2-structures and Spin+ 7 -structures in seven and eight dimensions. Formulae relating the covariant derivatives of the canonical forms and spinor fields are derived in each case. These are used to confirm the expected result that the form and spinorial classifications coincide. The mean curvature vector of associative and Cayley submanifolds of these spaces is calculated in terms of naturally-occurring tensor fields given by the structures. The final part of the thesis (comprising chapter 10) is an attempt to unify the first two parts. A certain `7-complex' quotient is described, which is analogous to the well-known hyper-Kahler quotient construction. This leads to insight into other possible interesting quotients which are correspondingly analogous to quaternionic-Kahler quotients, and these are speculated upon with a view to further research.en
dc.contributor.sponsorEngineering and Physical Sciences Research Council (EPSRC)en
dc.language.isoenen
dc.publisherThe University of Edinburghen
dc.subjectRiemannian submersionsen
dc.subjectconformal submersionsen
dc.subjectClifford algebraen
dc.subjectspinor bundlesen
dc.subjectDirac operatorsen
dc.subjectquaternionic-Kahler quotientsen
dc.titleOn conformal submersions and manifolds with exceptional structure groupsen
dc.typeThesis or Dissertationen
dc.type.qualificationlevelDoctoralen
dc.type.qualificationnamePhD Doctor of Philosophyen


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