Electronic Theses and Dissertations

Award/Availability

Open Access Thesis

Keywords

Einstein manifolds; Triangulation;

Abstract

Einstein metrics on manifolds are in some ways the "best" or most symmetric metrics those manifolds will allow. There has been much work on these metrics in the realm of smooth manifolds, and many results have been published. These results are very difficult to compute directly, however, and so it is helpful to consider piecewise-linear approximations to those manifolds in order to more quickly compute and describe what these metrics actually look like. We will use discrete analogues to powerful preexisting tools to do analysis on two particular triangulations of the three dimensional sphere with the intent of finding Einstein metrics on those triangulations. We find that, in one case, the intuitive solution we would expect from the literature holds, and in the other case it does not. We will discuss the differences between these two objects and will suggest possible avenues of research in the future.

Date of Award

2013

Degree Name

Master of Arts

Department

Department of Mathematics

First Advisor

Theron J. Hitchman

Date Original

2013

Object Description

1 PDF file (viii, 31 pages)

Language

EN

File Format

application/pdf

Included in

Mathematics Commons

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