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Full-Text Articles in Mathematics
Four-Dimensional Non-Reductive Homogeneous Manifolds With Neutral Metrics, Andrew Renner
Four-Dimensional Non-Reductive Homogeneous Manifolds With Neutral Metrics, Andrew Renner
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
A method due to É. Cartan was used to algebraically classify the possible four-dimensional manifolds that allow a (2, 2)-signature metric with a transitive group action which acts by isometries. These manifolds are classified according to the Lie algebra of the group action. There are six possibilities: four non-parameterized Lie algebras, one discretely parameterized family, and one family parameterized by R.
Lorentz Homogeneous Spaces And The Petrov Classification, Adam Bowers
Lorentz Homogeneous Spaces And The Petrov Classification, Adam Bowers
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
A. Z. Petrov gave a complete list of all local group actions on a four-dimensional space-time that admit an invariant Lorentz metric, up to an equivalence relation. His list was compiled by directly constructing all possible Lie algebras of infinitesimal generators of group actions that preserve a Lorentz metric. The goal of this paper was to verify that classification by algebraically constructing a list of all possible three-dimensional homogeneous spaces and calculating which among them have a non-degenerate invariant metric.