I've been browsing through MTW recently and I found something that puzzles me:(adsbygoogle = window.adsbygoogle || []).push({});

They claim that if you have two form, call it [itex]\mathbf{T}[/itex], it's value, say [itex]\mathbf{T}(\mathbf{u} , \mathbf{v} ) [/itex] can be represented geometrically as follows: take two vectors [itex]\mathbf{u}[/itex] and [itex]\mathbf{v}[/itex]; the surface containing those two is [itex]\mathbf{u} \bigwedge \mathbf{v}[/itex] (I don't get this, why isn't it just the vector product [itex] \mathbf{u} \times \mathbf{v}[/itex]?) and the value of the two form is just the number of tubes the "egg-crate" structure cuts through this parallelogram. I don't get this.

They also state that the a basis two-form, say [itex]\mathbf{d}x \bigwedge \mathbf{d}y[/itex] can be represented by just crossing the surfaces of each basis one-form. This is also confusing.

**Physics Forums | Science Articles, Homework Help, Discussion**

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!

# Geometric representation of two-forms.

Loading...

Similar Threads for Geometric representation forms |
---|

I Covariant Form of $E_{1}E_{2}|\vec{v}|$ |

I Geometric meaning of complex null vector in Newman-Penrose |

A Any 2-dimensional Lorentzian metric can be brought to this form? |

I Index gymnastics, matrix representations |

I 6-dimensional representation of Lorentz group |

**Physics Forums | Science Articles, Homework Help, Discussion**