Teaching-Liu


Home

Activities

Publications

Talks

Teaching

Research Seminars

Differential Geometry (H)

Fall 2025


Notices

2.

1. Tuesday Lecture room 5507: (14:00-15:35);Thursday Lecture room 5507: (07:50-09:25).


Lectures and excercises

Lecture 1概要:空间的弯曲.

Lecture 2 欧氏空间:向量运算、欧氏变换、向量分析、微分1形式 .

Lecture 3 欧氏空间上的微分形式和外微分运算.

Lecture 4 正则曲线. 平面曲线:密切圆和曲率;Frenet标架和带符号曲率;一般参数计算公式.

Lecture 5 平面曲线曲率的符号;平面曲线基本定理;空间曲线:密切平面与密切圆,Frenet标架和挠率.

Lecture 6 圆柱螺旋线;曲率和挠率的计算公式;挠率的几何意义;刚体运动不改变曲率和挠率.

Lecture 7 空间曲线的基本定理;正则曲面;切平面和法向量;例子.

Lecture 8 参数变换;第一基本形式;高斯曲率及其第一个显式公式.

Week 1

Homework 1.

Week 2

Homework 2.

Week 3

Homework 3.

Week 4

Homework 4.


References

1


Tutorials

Tutor

周驰宇


Geometric analysis on graphs 2025 Spring


Differential geometry (H) 2024 Fall


Discrete Ricci curvatures 2024 Spring


Differential geometry (H) 2023 Fall


Riemannian geometry 2023 Spring


Differential geometry (H) 2022 Fall


Riemannian geometry 2022 Spring


Geometric analysis on graphs 2021 Fall


Riemannian Geometry 2021 Spring


Differential Geometry 2020 Fall


Riemannian Geometry 2020 Spring


2017级华罗庚讨论班


Differential Geometry 2019 Fall


Riemannian Geometry 2019 Spring


Differential Geometry 2018 Fall


纯粹数学前沿


Riemannian Geometry 2018 Spring


Differential Geometry 2017 Fall


Riemannian Geometry 2017 Spring


Teaching in Durham