  Let $Q^N_l\subset \bC\bP^{N+1}$ denote the standard real, nondegenerate
hyperquadric of signature $l$ and $M\subset \bC^{n+1}$ a real, Levi
nondegenerate hypersurface of the same signature $l$. We shall assume that
there is a holomorphic mapping $H_0\colon U\to \bC\bP^{N_0+1}$, where $U$ is
some neighborhood of $M$ in $\bC^{n+1}$, such that $H_0(M)\subset Q^{N_0}_l$
but $H(U)\not\subset Q^{N_0}_l$. We show that if $N_0-n<l$ then, for any $N\geq
N_0$, any holomorphic mapping $H\colon U\to \bC\bP^{N+1}$ with $H(M)\subset
Q^{N}_l$ and $H(U)\not\subset Q^{N_0}_l$ must be the standard linear embedding
of $Q^{N_0}_l$ into $Q^N_l$ up to conjugation by automorphisms of $Q^{N_0}_l$
and $Q^N_l$.
