Symmetric Spaces, Geometric Manifolds and Geodesic Completeness
Date
2021
Authors
Munn, Thomas Jack
Editors
Advisors
Leistner, Thomas
Eastwood, Michael
Eastwood, Michael
Journal Title
Journal ISSN
Volume Title
Type:
Thesis
Citation
Statement of Responsibility
Conference Name
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.
School/Discipline
School of Mathematical Sciences
Dissertation Note
Thesis (MPhil) -- University of Adelaide, School of Mathematical Sciences, 2021
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