18.950 Differential Geometry, Spring 2005
Name
18-950Spring-2005/OcwWeb/Mathematics/18-950Spring-2005/CourseHome/index.htm
Size
12.68 KB
Format
HTML
Checksum (MD5)
5e05eaf2c903cb6304dfcd57b50c7681
Author(s)
Wickramasekera, Neshan Geethike
Alternative Title
Differential Geometry
Date Issued
June 2005
Abstract
This course is an introduction to differential geometry. Metrics, Lie bracket, connections, geodesics, tensors, intrinsic and extrinsic curvature are studied on abstractly defined manifolds using coordinate charts. Curves and surfaces in three dimensions are studied as important special cases. Gauss-Bonnet theorem for surfaces and selected introductory topics in special and general relativity are also analyzed. From the course home page: Course Description This course is an introduction to differential geometry of curves and surfaces in three dimensional Euclidean space. First and second fundamental forms, Gaussian and mean curvature, parallel transport, geodesics, Gauss-Bonnet theorem, complete surfaces, minimal surfaces and Bernstein's theorem are among the main topics studied.
Subjects
Metrics
Lie bracket
connections
geodesics
tensors
intrinsic and extrinsic curvature
defined manifolds using coordinate charts
Curves and surfaces in three dimensions
Gauss-Bonnet theorem for surfaces
general relativity
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Persistent DSpace Link
