Totally Nondegenerate Models and Standard Manifolds in CR Dimension One

Abstract

It is shown that two Levi–Tanaka and infinitesimal CR automorphism algebras, associated with a totally nondegenerate model of CR dimension one are isomorphic. As a result, the model surfaces are maximally homogeneous and standard. This gives an affirmative answer in CR dimension one to a certain question formulated by Beloshapka.

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Acknowledgements

The author expresses his sincere thanks to Mauro Nacinovich and Andrea Spiro for their helpful comments during the preparation of this paper. Also he would like to thank Valerii Beloshapka for his helpful discussions about the novelty of the problem, considered in this paper. The research of the author was supported in part by a Grant from IPM, no. 96510425.

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Correspondence to Masoud Sabzevari.

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Communicated by Fatemeh Helen Ghane.

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Sabzevari, M. Totally Nondegenerate Models and Standard Manifolds in CR Dimension One. Bull. Iran. Math. Soc. 46, 973–986 (2020). https://doi.org/10.1007/s41980-019-00305-4

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Keywords

  • CR manifolds
  • Total nondegeneracy
  • Standard manifolds
  • Tanaka prolongation

Mathematics Subject Classification

  • 32V40
  • 22F30