Spaces of Complex Null Geodesics in Complex-Riemannian Geometry

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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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