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We study the rigidity of holomorphic mappings from a neighborhood of aLevi-nondegenerate CR hypersurface $M$ with signature $l$ into a hyperquadric$Q_{l'}^{N} \subseteq \mathbb{CP}^{N+1}$ of larger dimension and signature. Weshow that if the CR complexity of $M$ is not too large then the image of $M$under any such mapping is contained in a complex plane with dimensionindependent of $N$. This result follows from two theorems, the firstdemonstrating that for sufficiently degenerate mappings, the image of $M$ iscontained in a plane, and the second relating the degeneracy of mappings intodifferent quadrics.

Partial Rigidity of CR Embeddings of Real Hypersurfaces into Hyperquadrics with Small Signature Difference