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