Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.652167
Title: Some problems in the invariant theory of parabolic geometries
Author: Harrison, Jonathan R.
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 1995
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Abstract:
The methods of Bailey, Eastwood and Graham for the parabolic invariant theory of conformal geometry are adapted to study the conformal polynomial invariants in the jets of differential forms, with analogous results being obtained. The methods of Bailey and Gover are then used to give the 'exceptional invariants'. These methods are extended to a different problem - that of the polynomial invariants in the jets of curves at a point, yielding complete results for a particular class of invariants. A construction was given by Graham, Jenne, Mason and Sparling of a set of conformally invariant, linear differential operators with leading term a power of the Laplacian, on general conformal manifolds. Their method involves the use of the 'ambient metric' construction. We give an alternative construction of most of these operators, using an invariant operator on the 'tractor bundle,' and describe the relationship between the tractor bundle and the ambient construction. We also relate these ideas to methods used by Wünsch to find some conformally invariant powers of the Laplacian. We introduce another parabolic geometry, not appearing previously in the literature, which we call contact-projective geometry. The flat model is sp(2n + 2,π) acting on π2n+1. The invariants of positively homogenous functions on the flat model are studied, using methods similar to those of the conformal case. We suggest a curved version of this geometry and describe the form of a tractor bundle - a vector bundle with connection and a skew-symmetric bi-linear form; and an ambient space - an affine manifold of one higher dimension equipped with a symplectic form.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.652167  DOI: Not available
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