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Transactions of the American Mathematical Society

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Spaces of complex null geodesics in complex-Riemannian geometry


Author: Claude LeBrun
Journal: Trans. Amer. Math. Soc. 278 (1983), 209-231
MSC: Primary 32G10; Secondary 32D15, 32L25, 53C22, 83C99
MathSciNet review: 697071
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Abstract: 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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DOI: https://doi.org/10.1090/S0002-9947-1983-0697071-9
Article copyright: © Copyright 1983 American Mathematical Society