MATH 4250/5250, Review for Final Exam

The folling items should be added to the reviews for Exam 1 and Exam 2.

The final will include problem sets 12, 13, and 14, lectures 4/15 - 4/30, and textbook sections 3.5, 5.1, 5.5, 6.1, 6.2, 6.3, 6.5.

Here is a list of definitions and theoremsyou should know for the exam that are not included in the review sheets for Exam 1 and Exam 2. You should know examples of each definition or theorem. (Examples can be found in the book, in homework, and in class notes.)

Definitions:

geodesic
geodesic curvature
surface area
total curvature (integral curvature)
covariant derivative (directional derivative)
parallel vector field
holonomy

Theorems:

If all points of M are umbilic, then M is part of a sphere or a plane.
If M is compact then K(p) > 0 for some point p of M.
If M is compact and K is constant, the K is part of a sphere.
Relation of holonomy and integral curvature.
Angle excess theorem for a geodesic triangle.