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To each complex composition algebra $\mathbb{A}$, there associates aprojective symmetric manifold $X(\mathbb{A})$ of Picard number one, which isjust 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 thesevarieties are rigid, namely for any smooth family of projective manifolds overa connected base, if one fiber is isomorphic to $X(\mathbb{A})$, then everyfiber is isomorphic to $X(\mathbb{A})$.

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