18.950 Differential Geometry, Spring 2005

Wickramasekera, Neshan Geethike

Author(s)

Wickramasekera, Neshan Geethike

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Alternative title

Differential Geometry

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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.

Date issued

2005-06

URI

http://hdl.handle.net/1721.1/49826

Department

Massachusetts Institute of Technology. Department of Mathematics

Other 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

Collections

Mathematics (18) - Archived