2000/01/11 by Alessandro Arsie, Arsie, Alessandro
Mathematics · Physics and Astronomy · #51P05 (Secondary) #53A40 #53C15 (Primary) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph) #math-ph #math.DG #math.MP #msc:51P05 #msc:53A40 #msc:53C15
paper · pdf · doi:10.48550/arxiv.math/0001060
9 pages
arxiv created 2000/01/11 · openalex publication_date 2000/01/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Having fixed a Kaehler class and the unique corresponding hyperkaehler metric, we prove that all special Lagrangian submanifolds of an irreducible symplectic 4-fold X are bi-Lagrangian and that they are obtained by complex submanifolds via a sort of "hyperkaehler rotation trick"; thus they retain part of the rigidity of complex submanifolds: indeed all special Lagrangian submanifolds of X turn out to be real analytic.