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Differential k-Form

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A differential k-form is a tensor of rank k that is antisymmetric under exchange of any pair of indices.

Differential k-form is a college-level concept that would be first encountered in a differential geometry course.

Prerequisites

Differential Geometry: Differential geometry is the field of mathematics that studies properties such as distance and curvature on surfaces and manifolds.
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.
Tensor: A tensor is a generalization of scalars, vectors, and matrices to an arbitrary number of indices.

Classroom Articles on Differential Geometry (Up to College Level)

  • Curvature
  • Mean Curvature
  • Gaussian Curvature