Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/134331
Type: | Thesis |
Title: | Symmetric Spaces, Geometric Manifolds and Geodesic Completeness |
Author: | Munn, Thomas Jack |
Issue Date: | 2021 |
School/Discipline: | School of Mathematical Sciences |
Abstract: | This thesis explores topics related to the geodesic completeness of compact locally sym metric Lorentzian manifolds. In particular, it discusses some important results relating to locally and globally symmetric spaces as well as the theory of geometric manifolds. These results are used to present a proof of a key proposition in Klingler (1996), which proves the geodesic completeness of compact Lorentzian manifolds with constant curvature. We also prove a new result, that compact Lorentzian manifolds which are locally isometric to the product of Cahen-Wallach space and flat Riemannian space are geodesically complete by extending methods used in Leistner & Schliebner (2016). These results may be helpful in the study of geodesic completeness of compact locally symmetric Lorentzian manifolds more generally as they reduce the number of open cases. |
Advisor: | Leistner, Thomas Eastwood, Michael |
Dissertation Note: | Thesis (MPhil) -- University of Adelaide, School of Mathematical Sciences, 2021 |
Keywords: | symmetric space geometry geodesic completeness Lorentzian |
Provenance: | This electronic version is made publicly available by the University of Adelaide in accordance with its open access policy for student theses. Copyright in this thesis remains with the author. This thesis may incorporate third party material which has been used by the author pursuant to Fair Dealing exceptions. If you are the owner of any included third party copyright material you wish to be removed from this electronic version, please complete the take down form located at: http://www.adelaide.edu.au/legals |
Appears in Collections: | Research Theses |
Files in This Item:
File | Description | Size | Format | |
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Munn2021_MPhil.pdf | 692.61 kB | Adobe PDF | View/Open |
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