18.950 2005春季课程：微分几何学(Differential Geometry, Spring 2005)
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在紧致可定向的曲面上的Gauss-Bonnet定理（感谢Neshan Wickramasekera博士的提供图片。）
The Gauss-Bonnet theorem for compact orientable surfaces. (Image by Dr. Neshan Wickramasekera.)
The Gauss-Bonnet theorem for compact orientable surfaces. (Image by Dr. Neshan Wickramasekera.)
课程重点
本课程包含一系列的相关阅读资料和完整的作业集。
This course features a set of readings, as well as a full set of assignments.
This course features a set of readings, as well as a full set of assignments.
课程描述
此课程介绍了三维欧氏空间上，曲线和曲面的微分几何。内容涵盖了第一和第二基本形式、高斯曲率（Gaussian curvature）和平均曲率、平行移动、测地线、Gauss-Bonnet定理（Gauss-Bonnet theorem）、完备曲面、极小曲面和Bernstein定理（Bernstein's theorem）等。
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.
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.
