2014/05/21 by Joël Merker, Merker, Joel, Samuel Pocchiola +3
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1405.5362
openalex publication_date 2014/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
On a real analytic 5-dimensional CR-generic submanifold M5 in C4 of\ncodimension 3, hence of CR dimension 1, which enjoys the generically satisfied\nnondegeneracy condition that Lie brackets up to length 3 of T1,0M generate\nCTM, a canonical Cartan connection is constructed after reduction to a certain\npartially explicit e-structure of the concerned local biholomorphic equivalence\nproblem. More advanced explorations of the incoming differential invariants due\nto the first and to the third authors already appeared in January 2014, hence\nthe purpose is to show, while studying this specific Class III-1 of\n5-dimensional CR structures, why and how the construction of Cartan geometries\nusually provides less information than a complete ramified discussion of\npotentially normalizable essential torsion coefficients.\n