In mathematics, a differentiable manifold
M
of dimension n is called parallelizable if there exist smooth vector fields
{
V
1
,
…
,
V
n
}
on the manifold, such that at any point
p
of
M
the tangent vectors
{
V
1
(
p
)
,
…
,
V
n
(
p
)
}
provide a basis of the tangent space at
p
. Equivalently, the tangent bundle is a trivial bundle, so that the associated principal bundle of linear frames has a section on
M
.
A particular choice of such a basis of vector fields on
M
is called a parallelization (or an absolute parallelism) of
M
.