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