In mathematics, a parallelization[1] of a manifold
of dimension n is a set of n global smooth linearly independent vector fields.
Given a manifold
of dimension n, a parallelization of
of n smooth vector fields defined on all of
denotes the fiber over
of the tangent vector bundle
A manifold is called parallelizable whenever it admits a parallelization.
A manifold
is parallelizable iff there is a diffeomorphism
ϕ :
ϕ
—is a linear map
ϕ
is parallelizable if and only if
is a trivial bundle.
is an open subset of
, i.e., an open submanifold of
is clearly parallelizable.