Nijenhuis tensors in pseudoholomorphic curves neighborhoods

2001/05/16 by Boris Kruglikov, Kruglikov, Boris
Mathematics · #53C15 #58H15 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.CV #math.DG #msc:53C15 #msc:58H15

paper · pdf · doi:10.48550/arxiv.math/0105130

27 pages

arxiv created 2001/05/16 · openalex publication_date 2001/05/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Normal forms of almost complex structures in a neighborhood of pseudoholomorphic curve are considered. We define normal bundles of such curves and study the properties of linear bundle almost complex structures. We describe 1-jet of the almost complex structure along a curve in terms of its Nijenhuis tensor. For pseudoholomorphic tori we investigate the problem of pseudoholomorphic foliation of the neighborhood. We obtain some results on nonexistence of the tori deformation.

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