Year

1995

Paper Type

Master's Thesis

College

College of Arts and Sciences

Degree Name

Master of Science in Mathematical Sciences (MS)

Department

Mathematics & Statistics

Committee Chairperson

Dr. Leonard Lipkin

Second Advisor

Dr. Jingcheng Tong

Rights Statement

http://rightsstatements.org/vocab/InC/1.0/

Third Advisor

Dr. Faiz Al-Rubaee

Abstract

In this thesis, the geometry of curved surfaces is studied using the methods of differential geometry. The introduction of manifolds assists in the study of classical two-dimensional surfaces. To study the geometry of a surface a metric, or way to measure, is needed. By changing the metric on a surface, a new geometric surface can be obtained. On any surface, curves called geodesics play the role of "straight lines" in Euclidean space. These curves minimize distance locally but not necessarily globally. The curvature of a surface at each point p affects the behavior of geodesics and the construction of geometric objects such as circles and triangles. These fundamental ideas of manifolds, geodesics, and curvature are developed and applied to classical surfaces in Euclidean space as well as models of non-Euclidean geometry, specifically, two-dimensional hyperbolic space.

Download

Included in

Mathematics Commons

Share

COinS
 

Accessibility Statement

This item was created or digitized before April 24, 2027, or is a reproduction of legacy material created before that date. It is preserved in its original, unmodified state specifically for research, reference, or historical recordkeeping. In accordance with the ADA Title II Final Rule, the Library provides accessible versions of archival materials by request. If you are experiencing difficulty accessing the information on the site due to a disability, please submit a request through the following form for assistance.