Dissertations and Theses @ UNI
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.
Year of Submission
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)
Copyright
©2013 Kyle Pitzen
Language
en
File Format
application/pdf
Recommended Citation
Pitzen, Kyle, "Einstein metrics on piecewise-linear three-spheres" (2013). Dissertations and Theses @ UNI. 83.
https://scholarworks.uni.edu/etd/83
