The tangent frame bundle (or simply the frame bundle) of a smooth manifold M is the frame bundle associated to the tangent bundle of M. The frame bundle of M is often denoted FM or GL(M) rather than F(TM). If M is n-dimensional then the tangent bundle has rank n, so the frame bundle of M is a principal GLn(R) bundle over M.
Read more about this topic: Frame Bundle
Famous quotes containing the words frame and/or bundle:
“He drew the curse upon the world, and cracked
The whole frame with his fall.
This made him long for home, as loth to stay
With murmurers and foes;”
—Henry Vaughan (1622–1695)
“We styled ourselves the Knights of the Umbrella and the Bundle; for, wherever we went ... the umbrella and the bundle went with us; for we wished to be ready to digress at any moment. We made it our home nowhere in particular, but everywhere where our umbrella and bundle were.”
—Henry David Thoreau (1817–1862)