Differential Geometry

Winter semester 2021
Course: MATH 4230
Course record number: 94917
Instructor: Y. Sommerhäuser
Schedule:
- Time: Tue 12:00 m-12:50 pm, Thu 12:00 m-12:50 pm, Fri 1:00 pm-1:50 pm
- Virtual room: Brightspace site of the course
Office hours of Y. Sommerhäuser:
- Time: Tue, Thu, 1:00 pm-3:00 pm and by appointment
- Virtual room: https://mun.webex.com/meet/sommerh
Textbook: M. Do Carmo: Differential Geometry of Curves and Surfaces, 2nd ed., Dover Publications, Mineola, 2016 (required resource)
Outline: The course begins with the theory of curves, especially the Frenet-Serret equations for curvature and torsion and the fundamental theorem of the local theory of curves. The course continues with the theory of surfaces, discussing the first and the second fundamental form, Gaussian curvature, Christoffel symbols, the 'theorema egregium', the Codazzi-Mainardi equations, the fundamental theorem of the local theory of surfaces, parallel displacement and geodesics, as well as the Gauss-Bonnet theorem.
Homework: Beginning Tuesday of the second week, a weekly exercise sheet will be distributed via e-mail. This has to be submitted on the following Tuesday via e-mail. There will be no exercise sheets during the last two weeks of the semester. In addition, a reading assignment from the textbook will be given in every lecture.
Examinations: There will be no examinations.
Final mark: The final mark will be based entirely on the score of the exercise sheets.
Policies: You are expected to participate in every class meeting, from the beginning to the end. Attendance will be recorded, but will not count towards the final mark.
Prerequisite: MATH 3202 (Vector Calculus)
Syllabus.
Exercise sheets:

Former courses
Last modified: March 27, 2021