In this section, we discuss briefly how to compare different almost complex structures on a manifold. Let M be a fixed compact manifold, TM its tangent bundle. Let J ∈ End(TM ) be an almost complex structure on M , with associated decomposition TM ⊗ C ' TM 0,1 ⊕ TM 1,0, and projections π0,1 and π1,0 to the two summands. Now suppose J ′ is a second almost complex structure. The reader should thi...
