Deformations of Complex Structures
نویسنده
چکیده
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 think of J ′ as a small deformation of the fixed almost complex structure J . If J ′ is “sufficiently close” to J , then π0,1 gives an isomorphism between TM 0,1 and TM 0,1, and we thus get a map
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