Sikorav, Jean-Claude Singularities of \(J\)-holomorphic curves. (English) Zbl 0886.30032 Math. Z. 226, No. 3, 359-373 (1997). 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 Cited in 9 Documents 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 PDFBibTeX XMLCite \textit{J.-C. Sikorav}, Math. Z. 226, No. 3, 359--373 (1997; Zbl 0886.30032) Full Text: DOI