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Differential K-form

Alternate names

alternating bilinear form | differential form | form | k-form | p-form

Basic definition

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

Detailed definition

A differential k-form is a tensor of tensor rank k that is antisymmetric under exchange of any pair of indices. The number of algebraically independent components in n dimensions is given by the binomial coefficient (n k). In particular, a one-form ω^1 (often simply called a "differential") is a quantity ω^1 = b_1 d x_1 + b_2 d x_2 + ... + b_n d x_n, where b_1 = b_1(x_1, x_2, ..., x_n), ..., b_n = b_n(x_1, x_2, ..., x_n) are the components of a covariant tensor.

Related terms

angle bracket | bra | covariant tensor | exterior algebra | exterior derivative | form integration | Hodge star | Jacobian | ket | manifold | one-form | Stokes' theorem | symplectic form | tangent bundle | tensor | wedge product

Educational grade level

college level

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