Exterior Powers
The k-th exterior power of the cotangent space, denoted Λk(Tx*M), is another important object in differential geometry. Vectors in the kth exterior power, or more precisely sections of the k-th exterior power of the cotangent bundle, are called differential k-forms. They can be thought of as alternating, multilinear maps on k tangent vectors. For this reason, tangent covectors are frequently called one-forms.
Read more about this topic: Cotangent Space
Famous quotes containing the words exterior and/or powers:
“There was never yet an uninteresting life. Such a thing is an impossibility. Inside of the dullest exterior there is a drama, a comedy, and a tragedy.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)
“He who is conversant with the supernal powers will not worship these inferior deities of the wind, waves, tide, and sunshine. But we would not disparage the importance of such calculations as we have described. They are truths in physics because they are true in ethics.”
—Henry David Thoreau (1817–1862)