Exterior Derivative
Consider a
Differential
k
-Form
(1)
Then its exterior derivative is
(2)
where
is the
Wedge Product
. Similarly, consider
(3)
Then
(4)
Denote the exterior derivative by
(5)
Then for a 0-form
,
(6)
for a 1-form
,
(7)
and for a 2-form
,
(8)
where
is the
Permutation Tensor
.
The second exterior derivative is
(9)
which is known as
Poincaré's Lemma
.
See also
Differential
k
-Form
,
Poincaré's Lemma
,
Wedge Product
© 1996-9
Eric W. Weisstein
1999-05-25