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


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.)
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