In mathematics, a coframe or coframe field on a smooth manifold
M
is a system of one-forms or covectors which form a basis of the cotangent bundle at every point. In the exterior algebra of
M
, one has a natural map from
v
k
:
⨁
k
T
∗
M
→
⋀
k
T
∗
M
, given by
v
k
:
(
ρ
1
,
…
,
ρ
k
)
↦
ρ
1
∧
…
∧
ρ
k
. If
M
is
n
dimensional a coframe is given by a section
σ
of
⨁
n
T
∗
M
such that
v
n
∘
σ
≠
0
. The inverse image under
v
n
of the complement of the zero section of
⋀
n
T
∗
M
forms a
G
L
(
n
)
principal bundle over
M
, which is called the coframe bundle.
