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:
“In vain to me the smiling Mornings shine,
And redd’ning Phoebus lifts his golden Fire:
The Birds in vain their amorous Descant join;
Or cheerful Fields resume their green Attire:”
—Thomas Gray (1716–1771)
“The My Lai soldier lifts me up again and again
and lowers me down with the other dead women and babies
saying, It’s my job. It’s my job.”
—Anne Sexton (1928–1974)
“Where the slow river
meets the tide,
a red swan lifts red wings
and darker beak.”
—Hilda Doolittle (1886–1961)