A Kähler potential is a locally defined real-valued function 
on a Kähler manifold
for which the Kähler form 
can be written as 
. Every
point has a neighborhood
on which such a potential exists, while a global Kähler potential requires additional
hypotheses. Here, the operators
 |
(1)
|
and
 |
(2)
|
are called the del and del bar operator, respectively.
For example, in 
, the function 
is a Kähler potential for
the standard Kähler form, because
 |  |  |
(3)
|
 |  |  |
(4)
|
 |  |  |
(5)
|
 |  |  |
(6)
|
