  We consider the class of Levi nondegenerate hypersurfaces $M$ in $\bC^{n+1}$
that admit a local (CR transversal) embedding, near a point $p\in M$, into a
standard nondegenerate hyperquadric in $\Bbb C^{N+1}$ with codimension $k:=N-n$
small compared to the CR dimension $n$ of $M$. We show that, for hypersurfaces
in this class, there is a normal form (which is closely related to the
embedding) such that any local equivalence between two hypersurfaces in normal
form must be an automorphism of the associated tangent hyperquadric. We also
show that if the signature of $M$ and that of the standard hyperquadric in
$\bC^{N+1}$ are the same, then the embedding is rigid in the sense that any
other embedding must be the original embedding composed with an automorphism of
the quadric.
