Topics in a Differential Geometry Course

To learn more about a topic listed below, click the topic name to go to the corresponding MathWorld classroom page.

Curvature	The amount of bending of a curve or surface. There are several different ways to measure curvature.
Differential Geometry	A field of mathematics that studies properties such as distance and curvature on surfaces and manifolds.
Differential k-Form	A tensor of rank k that is antisymmetric under exchange of any pair of indices.
Gaussian Curvature	One measure of the amount of "bending" a surface undergoes at a given point. The Gaussian curvature is independent of the coordinate system used to describe it.
Mean Curvature	The amount of "bending" of a surface at given point defined as the average of the two so-called "principal curvatures."
Tangent Bundle	Given a manifold, a new manifold that consists of the tangent spaces for each point pasted together in a continuous fashion.
Tensor	A generalization of scalars, vectors, and matrices to an arbitrary number of indices. MathWorld