Let Mββ be a smooth Levi-nondegenerate hypersurface of signature β
in Cn with nβ₯3, and write HβNβ for the standard
hyperquadric of the same signature in CN with Nβn<2nβ1β.
Let F be a holomorphic map sending Mββ into HβNβ. Assume F does
not send a neighborhood of Mββ in Cn into HβNβ. We show
that F is necessarily CR transversal to Mββ at any point. Equivalently,
we show that F is a local CR embedding from Mββ into HβNβ.Comment: To appear in Abel Symposia, dedicated to Professor Yum-Tong Siu on
the occasion of his 70th birthda