Date of Award

12-2011

Degree Type

Report

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Ian Anderson

Abstract

Four-dimensional space-times with symmetry play a central role in the theory of general relativity. In 1961, in the book Einstein Spaces, A.Z. Petrov gave a complete local classification of four-dimensional space-times based upon their local isometry group, that is, their Lie algebra of Killing vector fields. In this report we discuss algebraic and geometric properties of these Lie algebras. A database of these properties has been computed for the five-dimensional Lie algebras of Killing vectors found in Petrov. As an application of our work, we present dieomorphisms between a few pairs of these Lie algebras of Killing vectors.

Comments

This work made publicly available electronically on April 12, 2012.

Included in

Mathematics Commons

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