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, Volume 156, Issue 1–2, pp 57–61 | Cite as

Lorentzian CR structures and nonembeddability

  • Judith BrinkschulteEmail author
  • C. Denson Hill


In this paper we construct examples of CR deformations of Lorentzian hypersurfaces which are CR embeddable at all points outside an arbitrarily small compact set whose interior contains a point where CR embeddablity is not possible.

Mathematics Subject Classification

32V05 32V30 32G07 


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The first author was supported by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation, Grant BR 3363/2-1).


  1. 1.
    Andreotti, A., Hill, C.D., Levi, E.E.: Convexity and the Hans Lewy problem. Part II: Vanishing theorems. Ann. Sc. Norm. Super Pisa 26, 747–806 (1972)zbMATHGoogle Scholar
  2. 2.
    Brinkschulte, J., Hill, C.D.: Inflexible \(CR\) submanifolds. Math. Z. (2016). doi: 10.1007/s00209-016-1831-6 zbMATHGoogle Scholar
  3. 3.
    Dufresnoy, A.: Sur l’opérateur \(d^{\prime \prime }\) et les fonctions différentiables au sens de Whitney. Ann. Inst. Fourier 29, 229–238 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Hill, C.D.: Counterexamples to Newlander-Nirenberg up to the boundary. Proc. Symp. Pure Math. 52, 191–197 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Hill, C.D., Nacinovich, M.: Embeddable \(CR\) manifolds with nonembeddable smooth boundary. BUMI 7, 387–395 (1993)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Hill, C.D., Nacinovich, M.: Non completely solvable systems of complex first order PDE’s. Rend. Semin. Mat. Univ. Padova 129, 129–168 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Jacobowitz, H., Trèves, F.: Abberant \(CR\) structures. Hokkaido Math. J. 12, 276–292 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Jacobowitz, H., Trèves, F.: Erratum: abberant \(CR\) structures. Hokkaido Math. J. 42, 473–474 (2013)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Universität Leipzig, Mathematisches InstitutLeipzigGermany
  2. 2.Department of MathematicsStony Brook UniversityStony BrookUSA

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