Lifts
There are various ways to lift objects on M into objects on TM. For example, if c is a curve in M, then c' (the tangent of c) is a curve in TM. Let us point out that without further assumptions on M (say, a Riemannian metric), there is no similar lift into the cotangent bundle.
The vertical lift of a function is the function defined by, where is the canonical projection.
Read more about this topic: Tangent Bundle
Famous quotes containing the word lifts:
“Where the slow river
meets the tide,
a red swan lifts red wings
and darker beak.”
—Hilda Doolittle (1886–1961)
““... Anne has a way with flowers to take the place
Of what she’s lost: she goes down on one knee
And lifts their faces by the chin to hers
And says their names, and leaves them where they are.””
—Robert Frost (1874–1963)
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—Malcolm Muggeridge (1903–1990)