18.950 Differential Geometry, Spring 2005
Author(s)
Wickramasekera, Neshan Geethike
Download18-950Spring-2005/OcwWeb/Mathematics/18-950Spring-2005/CourseHome/index.htm (12.68Kb)
Alternative title
Differential Geometry
Metadata
Show full item recordAbstract
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.
Date issued
2005-06Department
Massachusetts Institute of Technology. Department of MathematicsOther identifiers
18.950-Spring2005
local: 18.950
local: IMSCP-MD5-3757ff62ab5d39b0498ac8cab0b4245d
Keywords
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