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Title: Einstein and conformally Einstein bi-invariant semi-Riemannian metrics
Author: Francis-Staite, Kelli L
Issue Date: 2015
School/Discipline: School of Mathematical Sciences
Abstract: This thesis considers the geometric properties of bi-invariant metrics on Lie groups. On simple Lie groups, we show that there is always an Einstein bi-invariant metric; that when the Lie algebra is of complex type, there is another metric on a simple Lie group that is Bach-flat but not conformally Einstein and that when the metric is a linear combination of these aforementioned metrics, that the metric is not Bach-flat. This result can be used to describe all bi-invariant metrics on reductive Lie groups. The thesis then considers bi-invariant metrics on Lie groups when the Lie algebra is created through a double extension procedure, as described initially by Medina [25]. We show two examples of bi-invariant metrics on non-reductive Lie groups that are Bach-flat but not conformally Einstein, however, we show that all Lorentzian bi-invariant metrics are conformally Einstein.
Advisor: Murray, Michael
Leistner, Thomas
Dissertation Note: Thesis (M.Phil.) -- University of Adelaide, School of Mathematical Sciences, 2015
Keywords: Einstein metrics
Einstein manifolds
Conformal Geometry
Back Tensor
semi-Riemannian geometry
Lie groups
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 exception. If you are the author of this thesis and do not wish it to be made publicly available or 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:
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