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:
“A day lays low and lifts up again all human things.”
—Sophocles (497–406/5 B.C.)
“Old politicians, like old actors, revive in the limelight. The vacancy which afflicts them in private momentarily lifts when, once more, they feel the eyes of an audience upon them. Their old passion for holding the centre of the stage guides their uncertain footsteps to where the footlights shine, and summons up a wintry smile when the curtain rises.”
—Malcolm Muggeridge (1903–1990)
“Where the slow river
meets the tide,
a red swan lifts red wings
and darker beak.”
—Hilda Doolittle (1886–1961)