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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Spaces of complex null geodesics in complex-Riemannian geometry
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by Claude LeBrun PDF
Trans. Amer. Math. Soc. 278 (1983), 209-231 Request permission


The notion of a complex - Riemannian $n$-manifold, meaning a complex $n$-manifold with a nondegenerate complex quadratic form on each tangent space which varies holomorphically from point to point, is briefly developed. It is shown that, provided $n \geqslant 4$, every such manifold locally arises canonically as the moduli space of all quadrics of a fixed normal-bundle type in an associated space of complex null geodesies. This relationship between local geometry and global complex analysis is stable under deformations.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 278 (1983), 209-231
  • MSC: Primary 32G10; Secondary 32D15, 32L25, 53C22, 83C99
  • DOI:
  • MathSciNet review: 697071