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:
“This idoll which you terme Virginitie,
Is neither essence subject to the eie,
No, nor to any one exterior sence,
Nor hath it any place of residence,
Nor is’t of earth or mold celestiall,
Or capable of any forme at all.”
—Christopher Marlowe (1564–1593)
“The shadow of a mighty Negro past flits through the tale of Ethiopia the shadowy and of the Egypt the Sphinx. Throughout history, the powers of single blacks flash here and there like falling stars, and die sometimes before the world has rightly gauged their brightness.”
—W.E.B. (William Edward Burghardt)