Complex Analytic Coordinates in Almost Complex Manifolds

1957/05/01 by August Newlander, Louis Nirenberg · 11 citations
Mathematics · #Algebraic and Geometric Analysis #Geometry #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Mathematical analysis #Mathematics #Pure mathematics

paper · doi:10.2307/1970051

openalex publication_date 1957/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15

Abstract

A manifold is called a complex manifold if it can be covered by coordinate patches with complex coordinates in which the coordinates in overlapping patches are related by complex analytic transformations. On such a manifold scalar multiplication by i in the tangent space has an invariant meaning. An even dimensional 2n real manifold is called almost complex if there is a linear transformation J defined on the tangent space at every point (and varying differentiably with respect to local coordinates) whose square is minus the identity, i.e. if there is a real tensor field h' satisfying

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