In mathematics, a vector-valued differential form on a manifold M is a differential form on M with values in a vector space V. More generally, it is a differential form with values in some vector bundle E over M. Ordinary differential forms can be viewed as R-valued differential forms. Vector-valued forms are natural objects in differential geometry and have numerous applications.
Read more about Vector-valued Differential Form: Formal Definition, Lie Algebra-valued Forms, Basic or Tensorial Forms On Principal Bundles
Famous quotes containing the words differential and/or form:
“But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.”
—Antonin Artaud (1896–1948)
“While they stand at home at the door he is dead already,
The only son is dead.
But the mother needs to be better,
She with thin form presently drest in black,
By day her meals untouch’d, then at night fitfully sleeping, often waking,
In the midnight waking, weeping, longing with one deep longing,
O that she might withdraw unnoticed, silent from life escape and
withdraw,
To follow, to seek, to be with her dear dead son.”
—Walt Whitman (1819–1892)