Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/49487
Type: | Thesis |
Title: | Invariant bilinear differential pairings on parabolic geometries. |
Author: | Kroeske, Jens |
Issue Date: | 2008 |
School/Discipline: | School of Mathematical Sciences : Pure Mathematics |
Abstract: | This thesis is concerned with the theory of invariant bilinear differential pairings on parabolic geometries. It introduces the concept formally with the help of the jet bundle formalism and provides a detailed analysis. More precisely, after introducing the most important notations and definitions, we first of all give an algebraic description for pairings on homogeneous spaces and obtain a first existence theorem. Next, a classification of first order invariant bilinear differential pairings is given under exclusion of certain degenerate cases that are related to the existence of invariant linear differential operators. Furthermore, a concrete formula for a large class of invariant bilinear differential pairings of arbitrary order is given and many examples are computed. The general theory of higher order invariant bilinear differential pairings turns out to be much more intricate and a general construction is only possible under exclusion of finitely many degenerate cases whose significance in general remains elusive (although a result for projective geometry is included). The construction relies on so-called splitting operators examples of which are described for projective geometry, conformal geometry and CR geometry in the last chapter. |
Advisor: | Eastwood, Michael |
Dissertation Note: | Thesis (Ph.D.) - University of Adelaide, School of Mathematical Sciences, 2008 |
Subject: | Conformal geometry. Invariants. Geometry, Projective. |
Keywords: | Parabolic geometry; Invariant operators: Conformal geometry; Projective geometry; CR geometry |
Appears in Collections: | Research Theses |
Files in This Item:
File | Description | Size | Format | |
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01front.pdf | 171.45 kB | Adobe PDF | View/Open | |
02whole.pdf | 760.31 kB | Adobe PDF | View/Open |
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