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)
|
