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:
“she drew back a while,
Then, yielding to the irresistible joy,
With frantic gesture and short breathless cry
Folded his frame in her dissolving arms.
Now blackness veiled his dizzy eyes, and night
Involved and swallowed up the vision; sleep,
Like a dark flood suspended in its course,
Rolled back its impulse on his vacant brain.”
—Percy Bysshe Shelley (1792–1822)
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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)