Integrability of almost complex structures on Banach manifolds

2004/07/23 by Daniel Beltiţă, Beltiţă, Daniel
Mathematics · #32Q60 #53C15 #58B12 #Differential Geometry (math.DG) #FOS: Mathematics #Functional Equations Stability Results #Nonlinear Differential Equations Analysis #Operator Algebras (math.OA) #advanced mathematical theories #math.DG #math.OA #msc:32Q60 #msc:53C15 #msc:58B12

paper · pdf · doi:10.48550/arxiv.math/0407395

13 pages

arxiv created 2004/07/23 · openalex publication_date 2004/07/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the classical integrability condition for almost complex structures on finite-dimensional smooth manifolds also works in infinite dimensions in the case of almost complex structures that are real analytic on real analytic Banach manifolds. As an application, we extend some known results concerning existence of invariant complex structures on homogeneous spaces of Banach-Lie groups.

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