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We study induced additive actions on projective hypersurfaces, i.e. regularactions of the algebraic group $\mathbb G_a^m$ with an open orbit that can beextended to a regular action on the ambient projective space. We prove that ifa projective hypersurface admits an induced additive action, then it is uniqueif and only if the hypersurface is non-degenerate. We also show that for any$n\geq 2$, there exists a non-degenerate hypersurface in $\mathbb P^n$ of eachdegree $d$ from $2$ to $n$.

Gorenstein Algebras and Uniqueness of Additive Actions