# Math 432 (01)-- Intro. To Diff. Geometry -- Spring 2020, Section 1

## This section

The instructor for this section is Professor Yanyan Li.

Office Hour: Thursday, 3:20pm to 4:40pm, Via Canvas Conference

## Textbook

Manfredo P. Do Carmo ; Differential Geometry of Curves and Surfaces (second edition);

## Policy

Homework (10%); Exam 1 (20%); Exam 2 (20%); Final Exam (50%). (for homework, the lowest will be dropped; no late homework)

## Tentative Syllabus and homework

Date Section Homework
Jan. 21 1.1, , 1.2, 1.3. Parametrized curves, regular curves and arc length 1.2: 1, 4, 5 1.3: 1, 3, 6
Jan. 23 1.4. The vector product in R^3 1.4: 3, 5
Jan. 28 1.5. The local theory of curves parametrized by arc length 1.5: 1, 2, 5, 9, 11, 12
Jan.30 1.7. Global properties of plane curves 1.7: 1, 2
Feb. 4 2.1, 2.2. Regular surfaces, inverse image of regular values 2.1: 2.2: 1, 2, 3, 5, 7
Feb. 6 2.3. Change of parameters; differentiable functions on surfaces 2.3: 2, 3, 4
Feb. 11 2.4. The tangent plane; the differential of a map 2.4: 1, 2, 3, 4, 6
Feb. 13 2.5. The first fundamental form; area 2.5: 1, 2, 4, 5, 10
Feb. 18 2.5 and 3.1.
Feb. 20 Review for the Exam 1
Feb. 25 Exam 1
Feb. 27 3.2. The definition of Gauss map and its fundamental properties 3.2: 1, 2, 3, 5, 6, 7, 8, 11, 12.
March 3 3.3. The Gauss map in local coord. 3.3: 1, 4, 5
March 5 3.3. The Gauss map in local coord. 3.3: 6, 7, 13, 14
March 10 3.4. Vector fields 3.4: 1, 3, 4, 5, 6, 10
March 12 Cancelled by the University
March 24 3.5. Ruled surfaces and minimal surfaces 3.5: 2, 3, 4, 6
March 26 3.5. and 4.1. 3.5: 11, 12
March31 4.2. Isometries; conformal maps 4.2: 1, 2, 3, 7.
April 2 Exam 2
April 7 4.3. The Gauss theorem and the equation of compatibility 4.3: 1, 3, 4, 5, 6, 7, 8
April 9 4.4. Parallel transport, geodesics 4.4: 1, 2, 3, 4, 5
April 14 4.4. Parallel transport, geodesics 4.4: 7, 14
April 16 4.4. Parallel transport, geodesics 4.4: 17
April 21 4.5. The Gauss-Bonnet theorem and its applications 4.5: 1, 2, 3, 4
April 23 4.6. The exponential map, geodesic polar coordinates 4.6: 1, 2, 3, 4, 5
April 28 4.6. The exponential map, geodesic polar coordinates 4.6:
April 30 Review for the Final Exam