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Transactions of the American Mathematical Society

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Holomorphic curves in Lorentzian CR-manifolds


Author: Robert L. Bryant
Journal: Trans. Amer. Math. Soc. 272 (1982), 203-221
MSC: Primary 32F25; Secondary 53C40
DOI: https://doi.org/10.1090/S0002-9947-1982-0656486-4
MathSciNet review: 656486
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Abstract: A CR-manifold is said to be Lorentzian if its Levi form has one negative eigenvalue and the rest positive. In this case, it is possible that the CR-manifold contains holomorphic curves. In this paper, necessary and sufficient conditions are derived (in terms of the "derivatives" of the CR-structure) in order that holomorphic curves exist. A "flatness" theorem is proven characterizing the real Lorentzian hyperquadric $ {Q_5} \subseteq {\mathbf{C}}{P^3}$, and examples are given showing that nonflat Lorentzian hyperquadrics can have a richer family of holomorphic curves than the flat ones.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1982-0656486-4
Keywords: Prolongation, CR-structure, Levi form, holomorphic curve, Lorentzian hyperquadric
Article copyright: © Copyright 1982 American Mathematical Society