About $c$-rigid quadrics

In the article strongly nondegenerate $(k,n)$-quadrics all of whose linear automorphisms are of the form $z\to\mu z$, $w\to|\mu|^2w$, $\mu\in\mathbb C\setminus\{0\}$ are considered. Quadrics all of whose linear automorphisms are of this form were called $c$-rigid by V. Beloshapka. The main result of the article is the following: any $c$-rigid strongly nondegenerate $(k,n)$-quadric has no nonlinear automorphisms. A table indicating the relationship between linear and nonlinear automorphisms for $(k,n)$-quadrics is presented.