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.
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Famous quotes containing the words frame and/or bundle:
“Human life itself may be almost pure chaos, but the work of the artist—the only thing he’s good for—is to take these handfuls of confusion and disparate things, things that seem to be irreconcilable, and put them together in a frame to give them some kind of shape and meaning. Even if it’s only his view of a meaning. That’s what he’s for—to give his view of life.”
—Katherine Anne Porter (1890–1980)
““There is Lowell, who’s striving Parnassus to climb
With a whole bale of isms tied together with rhyme,
He might get on alone, spite of brambles and boulders,
But he can’t with that bundle he has on his shoulders,
The top of the hill he will ne’er come nigh reaching
Till he learns the distinction ‘twixt singing and preaching;”
—James Russell Lowell (1819–1891)