Would the following be an accurate dictionary-style summary of the various (conflicting) uses of the word form? (The vector space with respect to which the tensors and tensor fields in 2 and 3 are defined is the tangent space of a manifold.)(adsbygoogle = window.adsbygoogle || []).push({});

(1) As in everyday, non-jargon English, one of several ways of expressing an idea. E.g. "The differential form of Maxwell's equations."

(2) (a) A covariant tensor. (b) A covariant tensor field. E.g. "A metric tensor is defined to be a nondegenerate symmetric bilinear form on each tangent space that varies smoothly from point to point."

(3) (a) A totally antisymmetric covariant tensor, i.e. a covariant tensor whose value changes sign when any pair of arguments are interchanged. (b) A totally antisymmetric covariant tensor field. (With "differential form" meaning a differentiable form in this sense, e.g. "If [itex]\omega |_p[/itex] is differentiable, then we will refer to it as adifferentialform.")

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Defining forms

Loading...

Similar Threads - Defining forms | Date |
---|---|

I Getting a matrix into row-echelon form, with zero-value pivots | Feb 17, 2018 |

I How this defines a linear transformation | Apr 25, 2016 |

Equality of two elements of a hilbert space defined? | Aug 1, 2015 |

Operators for comparing superposition components -- definable? | Apr 6, 2015 |

Defining Functions on Tensor Products | May 23, 2014 |

**Physics Forums - The Fusion of Science and Community**