Moving Tangent Frames
The most commonly encountered case of a moving frame is for the bundle of tangent frames (also called the frame bundle) of a manifold. In this case, a moving tangent frame on a manifold M consists of a collection of vector fields X1, X2, ..., Xn forming a basis of the tangent space at each point of an open set U ⊂ M.
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Famous quotes containing the words moving and/or frames:
“What have we achieved in mowing down mountain ranges, harnessing the energy of mighty rivers, or moving whole populations about like chess pieces, if we ourselves remain the same restless, miserable, frustrated creatures we were before? To call such activity progress is utter delusion. We may succeed in altering the face of the earth until it is unrecognizable even to the Creator, but if we are unaffected wherein lies the meaning?”
—Henry Miller (1891–1980)
“In frames as large as rooms that face all ways
And block the ends of streets with giant loaves,
Screen graves with custard, cover slums with praise
Of motor-oil and cuts of salmon, shine
Perpetually these sharply-pictured groves
Of how life should be.”
—Philip Larkin (1922–1986)