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:
“Consider a man riding a bicycle. Whoever he is, we can say three things about him. We know he got on the bicycle and started to move. We know that at some point he will stop and get off. Most important of all, we know that if at any point between the beginning and the end of his journey he stops moving and does not get off the bicycle he will fall off it. That is a metaphor for the journey through life of any living thing, and I think of any society of living things.”
—William Golding (b. 1911)
“For laughter frames the lips of death—
Death frames the Singer and the Song.”
—Allen Tate (1899–1979)