  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 ${\rm Lag}(3,6),
{\rm Gr}(3,6), \mathbb{S}_6, E_7/P_7.$ 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 $X(\mathbb{A})$.
