Differential Geometry
(Math 421)
Spring 2023
Instructor:
Paul Aspinwall
Credits: 1.0
Time: Mon and Wed 10:15am - 11:30am
Location:
Homework
Prerequisites
- (Math 221 or Math 218) and (Math 212 or Math 222) or consent of instructor.
Evaluations
- Homework (15%+5%): Some longer homeworks may count extra towards the final grade.
- Quiz (5%): Occasionally in class
- Midterm (25%): February 27 in class
- Final (50%): Saturday May 6, 9:00am
Office Hours
- Tuesday 1:30-2:30PM
- Thursday 10:00-11:00AM
Synopsis
- Curves in R3
- Curvature and Torsion
- Frenet Frame
- Surfaces in R3
- First Fundemental Form
- Gauss map and the second fundamental form
- Codazzi and Gauss equations
- Covariant deriavtives and geodesics
- Holonomy and the Gauss-Bonnet formula
- Differential Forms
- Riemannian Geometry in Higher dimensions.
Textbooks
The course will be mainly based on the notes by Shifrin but I may also use
some of O'Neill:
- Theodore Shifrin, Differential Geometry: A First Course in Curves and
Surfaces. Online Notes.
- B. O'Neill, Elementary Differential Geometry,
Second Edition 2006, Elsevier.
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