Differential Geometry

Department: 
MATH
Course Number: 
4441
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Every fall semester

The theory of curves, surfaces, and more generally, manifolds. Curvature, parallel transport, covariant differentiation, Gauss-Bonet theorem

Prerequisites: 

MATH 2401 or MATH 2411 or MATH 24X1 or MATH 2551 or MATH 2561 or MATH 2X51

Course Text: 

No text

Topic Outline: 
  • Part (1): Theory of Curves Curves in R^2 and R^3 Velocity, speed, arclength, acceleration Curvature, torsion, the moving trihedron Frenet-Serret equations
  • Part (2): Theory of Surfaces Regular surfaces in R^3 First and Second Fundamental Forms, the mean and Gaussian curvatures Gauss-Weingarten equations, Gauss's Theorema Egregium Introduction to Tensors, Their use in the theory of surfaces Intrinsic geometry of surfaces, geodesic curvature, geodesic coordinates, Gauss-Bonnet Theorem