The differential forms on decompose into forms of type , sometimes called -forms. For example, on , the exterior algebra
decomposes into four types:

(1)

(2)

where ,
, and denotes the direct sum.
In general, a -form
is the sum of terms with s and s.
A -form decomposes into a sum of -forms, where .

For example, the 2-forms on decompose as

(3)

(4)

The decomposition into forms of type is preserved by holomorphic
functions. More precisely, when is holomorphic and is a -form on , then the pullback is a -form on .