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Differential Geometry

Explore DifferentialGeometry on MathWorld


Differential geometry is the field of mathematics that studies properties such as distance and curvature on surfaces and manifolds.

Differential geometry is a college-level concept and course.

Prerequisites

Manifold: A manifold is a topological space that is locally Euclidean, i.e., around every point, there is a neighborhood that is topologically the same as an open unit ball in some dimension.
Surface: A surface is a two-dimensional piece of three-dimensional space.
Topology: (1) As a branch of mathematics, topology is the mathematical study of object's properties that are preserved through deformations, twistings, and stretchings. (2) As a set, a topology is a set along with a collection of subsets that satisfy several defining properties.

Classroom Articles on Differential Geometry (Up to College Level)

  • Curvature
  • Gaussian Curvature
  • Differential k-Form
  • Mean Curvature