Rigidity of projective symmetric manifolds of Picard number 1 associated to composition algebras

To each complex composition algebra $\mathbb{A}$, there associates a projective symmetric manifold $X(\mathbb{A})$ of Picard number one, which is just a smooth hyperplane section of the following varieties $\mathrm{L}\mathrm{a}\mathrm{g}(3,6),\mathrm{G}\mathrm{r}(3,6),{\mathbb{S}}_6,E_7\mathrm{/}{P}_7\mathrm{.}$ In this paper, it is proven that these varieties are rigid, namely for any smooth family of projective manifolds over a connected base, if one fiber is isomorphic to $X(\mathbb{A})$, then every fiber is isomorphic to $X(\mathbb{A})$.