Curvature Form
The curvature form of a principal G-connection ω is the -valued 2-form Ω defined by
It is G-equivariant and horizontal, hence corresponds to a 2-form on M with values in . The identification of the curvature with this quantity is sometimes called the second structure equation.
Read more about this topic: Connection (principal Bundle)
Famous quotes containing the word form:
“I sometimes wonder that we can be so frivolous ... as to attend to the gross but somewhat foreign form of servitude called Negro Slavery, there are so many keen and subtle masters that enslave both north and south. It is hard to have a southern overseer; it is worse to have a northern one; but worst of all when you are the slave-driver of yourself.”
—Henry David Thoreau (1817–1862)