On the CR transversality of holomorphic maps into hyperquadrics

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Let Mℓ be a smooth Levi-nondegenerate hypersurface of signature ℓ in Cⁿ with n≥ 3, and write Hℓⁿ for the standard hyperquadric of the same signature in Cⁿ with N-n< n-1/2. Let F be a holomorphic map sending Mℓ into Hℓⁿ. Assume F does not send a neighborhood of Mℓ in Cⁿ into Hℓⁿ. We show that F is necessarily CR transversal to Mℓ at any point. Equivalently, we show that F is a local CR embedding from Mℓ into Hℓⁿ.