On the embeddability of real hypersurfaces into hyperquadrics

In this paper, we provide effective results on the non-embeddability of real-analytic hypersurfaces into a hyperquadric. We show that, under the codimension restriction N≤2n, the defining functions φ(z,z¯,u) of all real-analytic hypersurfaces M={v=φ(z,z¯,u)}⊂Cn+1 containing Levi-nondegenerate points and locally transversally holomorphically embeddable into some hyperquadric Q⊂CN+1 satisfy an universal algebraic partial differential equation D(φ)=0, where the algebraic-differential operator D=D(n,N) depends on n≥1, n