Definition
Let G be a Lie group with Lie algebra, and P → B be a principal G-bundle. Let ω be an Ehresmann connection on P (which is a -valued one-form on P).
Then the curvature form is the -valued 2-form on P defined by
Here stands for exterior derivative, is defined by and D denotes the exterior covariant derivative. In other terms,
Read more about this topic: Curvature Form
Famous quotes containing the word definition:
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
—Adrienne Rich (b. 1929)
“It is very hard to give a just definition of love. The most we can say of it is this: that in the soul, it is a desire to rule; in the spirit, it is a sympathy; and in the body, it is but a hidden and subtle desire to possess—after many mysteries—what one loves.”
—François, Duc De La Rochefoucauld (1613–1680)
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)