LeBrun's nonrealizability theory in higher dimensions (Q1063147)

In this article, the assertions made by \textit{C. R. LeBrun} in the last paragraph of his paper in Trans. Am. Math. Soc. 278, 209-231 (1983; Zbl 0562.53018) are verified. Associated to every Riemannian manifold (M,g) is a CR manifold N, where N is the space of g-isotropic lines in the complexified cotangent bundle \(T^*M\) and the distribution defining the CR structure is given by the vanishing of the canonical symplectic form on \(T^*M\). It is shown that N is determined only by the conformal structure underlying (M,g), and N can be locally embedded in a complex manifold if and only if (M,g) is conformally equivalent to a real- analytic Riemannian manifold.