# Integrability of an almost complex structure vs holomorphity of the \$ M rightarrow mathcal {J} (M) \$ section

Let's say we have an almost complex variety. $$(M, J)$$. Consider the complex vector package $$V rightarrow M$$ whose fiber over $$x$$ It is the space of almost complex structures on $$T_x M$$.

Is there any logical connection between the following two conditions:

• $$J$$ it is integrable;
• the map $$M rightarrow V$$ associated to $$J$$ Is it holomorphic?