Adventures and Misadventures in Riemannian Geometry Curvature Comparisons for Surfaces of Revolution
Date of Award
2005
Document Type
Thesis
Degree Name
Bachelors
Department
Natural Sciences
First Advisor
McDonald, Patrick
Keywords
Surfaces of Revolution, Curvature Comparisons, Riemannian Geometry
Area of Concentration
Mathematics
Abstract
We introduce important tools of differential and Riemannian geometry, focusing on the construction of smooth manifolds, Riemannian metrics, geodesics, curvature,and the Laplace operator. We use the example of a surface of revolution throughout, providing a comprehensible but non-trivial case for consideration. We conclude by introducing a fundamental comparison theorem involving curvature bounds, and apply this result to surfaces of revolution.
Recommended Citation
Silverstein, Jake, "Adventures and Misadventures in Riemannian Geometry Curvature Comparisons for Surfaces of Revolution" (2005). Theses & ETDs. 3580.
https://digitalcommons.ncf.edu/theses_etds/3580
Rights
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.