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 1:302:30PM
 Thursday 10:0011:00AM
Synopsis
 Curves in R^{3}
 Curvature and Torsion
 Frenet Frame
 Surfaces in R^{3}
 First Fundemental Form
 Gauss map and the second fundamental form
 Codazzi and Gauss equations
 Covariant deriavtives and geodesics
 Holonomy and the GaussBonnet 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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