teaching
The course Qi served as TA in fall 2022
Differential Geometry fall 2022
Lecturer: Yongbin Zhang
TAs: Ziwei Lu, Qi Zhang
Main:
-
- 微分几何, 彭家贵/陈卿
- The traditional book at USTC for a long time.
Reference:
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- 微分几何初步, 陈维桓
- A good book for a good begining.
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- Differential Geometry of Curves & Surfaces, Manfredo P.Do Carmo
- Reference book world wide.
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- Differential Geometry, Loring W. Tu, GTM275
- A good book from perspect of manifolds.
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- An introduction to manifolds, Loring W. Tu
- A good reference to manifolds.
Other courses:
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- 2017 Fall, 2022 Fall(H) , Differential Geometry at USTC.
- Given by Prof. Shipin Liu.
Lecture Notes， Homework and Solutions
| Lecture | Time | Course | Homeworks | Solutions | ||||
|---|---|---|---|---|---|---|---|---|
| Lec1 | Week1 | Eucelidean space | - | - | ||||
| Lec2 | Week1 | Curves in $E^n$ | ex1[2,3] | - | ||||
| Lec3 | Week2 | Holiday | - | - | ||||
| Lec4 | Week2 | Holiday | - | - | ||||
| Lec5 | Week2 | Concept of a surface | ex2[1(2,4), 2, 3, 8, 13(2), 18(1)] | - | ||||
| Lec6 | Week3 | The first fundamental form of surfaces | ex2[4(1,3), 5, 9, 12, 15, 16] | - | ||||
| Lec7 | Week3 | The second fundamental form of surfaces | ex2[17, 20, 21] | - | ||||
| Lec8 | Week4 | Principle curvanture | ex3[1(1,5), 2, 3, 4, 5] | - | ||||
| Lec9 | Week4 | Weingarten transformation | - | - | ||||
| Lec10 | Week5 | Gaussian curvature and mean curvature | ex3[7,8(2), 9, 10, 12] | - | ||||
| Lec11 | Week5 | Examples of surface | ex3[14, 15, 16] | - | ||||
| Lec12 | Week6 | review | - | - | ||||
| Lec13 | Week6 | midterm exam | - | - | ||||
| Lec14 | Week7 | Natural frame of surfaces | ex3[18, 20, 24, 31] | - | ||||
| Lec15 | Week7 | Gauss-Codazzi equation | ex3[17, 19, 22, 25, 27] | - | ||||
| Lec16 | Week8 | Existence and uniqueness of surfaces | ex3[29, 35] | - | ||||
| Lec17 | Week8 | Moving-frame using differential forms | - | - | ||||
| Lec18 | Week9 | Concept of differential forms | ex3[32,33,36] | - | ||||
| Lec19 | Week9 | Intrinsic transformations between surfaces | ex4[1,2,4,5] | - | ||||
| Lec20 | Week10 | Covarient derivative of surfaces | ex4[6,8] | - | ||||
| Lec21 | Week10 | Geodics and distance on surfaces | ex4[9,12] | - | ||||
| Lec22 | Week11 | Atlas of geodics | ex4[15,16,18] | - | ||||
| Lec23 | Week11 | Gauss-Bonnet theorem | ex4[14] | - |