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IPM
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“School of Mathematics”

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Paper   IPM / M / 15518
School of Mathematics
  Title:   Biholomorphic equivalence to totally nondegenerate model CR manifolds
  Author(s):  Msoud Sabzevari
  Status:   Published
  Journal: Annali di Matematica Pura ed Applicata
  Vol.:  198
  Year:  2019
  Pages:   1121-1163
  Supported by:  IPM
  Abstract:
Applying Elie Cartan�??s classical method, we show that the biholomorphic equivalence problem to a totally nondegenerate Beloshapka�??s model of CR dimension one and codimension k > 1, whence of real dimension 2 + k, is reducible to some absolute parallelism, namely to an e-structure on a certain prolonged manifold of real dimension either 3 + k or 4 + k. The proof relies upon a weight analysis on the structure equations associated with the mentioned problem of equivalence. As a consequence of the achieved results, we also confirm in CR dimension one Beloshapka�??s maximum conjecture on the rigidity of his models of certain lengths equal or greater than three.

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