First,let me state the question:
Let $M$ be the real manifold described as a hypersurface $x_0^4+x_1^4+x_2^4+x_3^4=0$ in $\mathbb P^3$.We denote the naturally induced complex structure by $I$.Show that $(M,I)$ and $(M,-I)$ define isomorphic manifolds.
As far as I know,the oriented dimension two differentiable manifolds (Riemannian surface) have naturally almost complex structures(and also integrable,then determine complex structures).So,
1.Should I show the orientability of $M$?If yes,I notice this post: Hypersurface orientable if it admits a smooth normal vector field .I think it can work.
2.How can I show two two almost complex structure define isomorphic complex manifolds?
Any advice and references will be appriecated.Thanks a lot.
Here's the best answer I can come up with. The problem as you posed it is vacuous. If $M=\Bbb C$, then $f(z)=\bar z$ is a pseudo-holomorphic map from $(M,I)$ to $(M,-I)$. More generally, if you have a complex submanifold of $\Bbb C^n$ or of $\Bbb CP^n$ that is given by real equations (homogeneous equations, of course, in the projective case), then this construction may still work (the mapping preserves the submanifold, but you have work to do to check what happens to tangent vectors).