Geodesic
Hassett-Tschinkel correspondence and automorphisms of the quadric
Sbornik. Mathematics, Tome 200 (2009) no. 11, pp. 1715-1729

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In this paper we study locally transitive actions of the commutative unipotent group $\mathbb G_a^n$ on a nondegenerate quadric in the projective space $\mathbb P^{n+1}$. It is shown that for each $n$ such an action is unique up to isomorphism. Bibliography: 9 titles.
Keywords: automorphisms of quadrics, locally transitive actions. 
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     author = {E. V. Sharoiko},
     title = {Hassett-Tschinkel correspondence and automorphisms of the quadric},
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E. V. Sharoiko. Hassett-Tschinkel correspondence and automorphisms of the quadric. Sbornik. Mathematics, Tome 200 (2009) no. 11, pp. 1715-1729. http://geodesic.mathdoc.fr/item/SM_2009_200_11_a5/