Spring 2021 Differential Geometry

Reference：

Books
【1】《An Introduction to Manifolds》 by  Loring W. Tu
【2】《Introduction to smooth manifolds》by John M. Lee
【3】《微分几何讲义》 by 陈省身 陈维桓

Preliminary: Mathematical analysis, Linear algebra, Point set topology.

Note (PDF version, not finished)

• Week 10: 微分流形
• Week 11: 向量场与切丛
• Week 12: 微分形式与外微分
• Week 13: 向量丛与联络
• Week 14: 积分与Stokes公式
• Week 15-16: 黎曼度量与测地线
• Week 17: 黎曼曲率与Gauss-Bonnet公式