Relative extension of a compatible almost complex structure
= Relative extension of a compatible almost complex structure
If a compatible almost complex structure is prescribed along a closed <symplectic submanifold> $N\subset M$ and preserves $TN$, it extends to one on $M$. Choose a compatible structure separately on $TN$ and its <symplectic normal bundle>, use the associated metric along $N$, extend that metric to $M$, and apply the <metric construction of a compatible almost complex structure>.