## Singularities of $$J$$-holomorphic curves.(English)Zbl 0886.30032

We prove a result of M. Micallef and B. White: a germ of $$J$$-holomorphic curve in an almost complex manifold is $$C^1$$-equivalent to a germ of complex curve in $$\mathbb{C}^n$$. We give an example showing that this cannot be improved to $$C^2$$ even if $$J$$ is real analytic. Finally we deduce a global version: for every $$J$$-curve there is a complex structure on some neighbourhood with respect to which the curve is still complex.
Reviewer: A.R.Cane

### MSC:

 30G20 Generalizations of Bers and Vekua type (pseudoanalytic, $$p$$-analytic, etc.) 32S99 Complex singularities 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)

### Keywords:

$$J$$-holomorphic curves; complex manifolds; singularities
Full Text: