2016/01/06 by Masoud Sabzevari, Sabzevari, Masoud
Mathematics · #32V40 #57S25 #58A15 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1601.01164
openalex publication_date 2016/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Applying Elie Cartan's classical method, we show that the biholomorphic\nequivalence problem to a totally nondegenerate Beloshapka's model of CR\ndimension one and codimension k> 1, whence of real dimension 2+k, is\nreducible to some absolute parallelism, namely to an e-structure on a certain\nprolonged manifold of real dimension either 3+k or 4+k. The proof relies on\nthe weight analysis of the structure equations associated with the mentioned\nproblem of equivalence. Thanks to the achieved results, we prove Beloshapka's\nmaximum conjecture about the rigidity of his CR models of certain lengths equal\nor greater than three: "CR automorphism Lie groups of these models do not\ncontain any nonlinear map, preserving the origin". Here, we mainly deal with CR\nmodels of the fixed CR dimension one though the results seem generalizable by\nmeans of certain analogous proofs.\n