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2 results

  • CANCELLING COMPLEX POINTS IN CODIMENSION TWO

  • Part of
  • MARKO SLAPAR
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 88 / Issue 1 / August 2013
    Published online by Cambridge University Press:
    09 August 2012, pp. 64-69
    Print publication:
    August 2013
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  • A generically embedded real submanifold of codimension two in a complex manifold has isolated complex points that can be classified as either elliptic or hyperbolic. In this paper we show that a pair consisting of one elliptic and one hyperbolic complex point of the same sign can be cancelled by a $\mathcal {C}^{0}$small isotopy of embeddings.

  • CR Mappings of Circular CR Manifolds

  • André Boivin, Roman Dwilewicz
  • Journal:
    Canadian Mathematical Bulletin / Volume 38 / Issue 4 / 01 December 1995
    Published online by Cambridge University Press:
    20 November 2018, pp. 396-407
    Print publication:
    01 December 1995
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  • Let M be a circular CR manifold and let N be a rigid CR manifold in some complex vector spaces. The problem of the existence of local CR mappings from M into N is considered. Conditions are given which ensure that the space of such CR mappings depends on a finite number of parameters. The idea of the proof of the main result relies on a Bishop type equation for CR mappings. Roughly speaking, we look for CR mappings from M into N in the form F = (ƒ,g), we assume that g is given, then we find ƒ in terms of g and some parameters, and finally we look for conditions on g. It works independently of assumptions on the Levi forms of M and N, and there is also some freedom on the codimension of the manifolds.