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:
“Professor Eucalyptus said, “The search
For reality is as momentous as
The search for god.” It is the philosopher’s search
For an interior made exterior
And the poet’s search for the same exterior made
Interior: breathless things broodingly abreath....”
—Wallace Stevens (1879–1955)
“The powers of the federal government ... result from the compact to which the states are parties, [and are] limited by the plain sense and intention of the instrument constituting that compact.”
—James Madison (1751–1836)