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:
“From Harmony, from heavenly Harmony
This universal Frame began:
From Harmony to Harmony
Through all the Compass of the Notes it ran,
The Diapason closing full in Man.”
—John Dryden (1631–1700)
““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)