Geodesic
Real quadrics of codimension 3 in~$\mathbb C^6$ and their non-linear automorphisms
Izvestiya. Mathematics , Tome 59 (1995) no. 3, pp. 597-617.

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In this paper, non-degenerate $(3,3)$-quadrics are considered. A list of quadrics with non-linear automorphisms is obtained up to equivalence. All nullquadrics of codimension 3 in $\mathbb C^6$ are determined. We give an example of a quadric with a non-linear automorphism not representable as a Poincare automorphism. 
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N. F. Palinchak. Real quadrics of codimension 3 in~$\mathbb C^6$ and their non-linear automorphisms. Izvestiya. Mathematics , Tome 59 (1995) no. 3, pp. 597-617. http://geodesic.mathdoc.fr/item/IM2_1995_59_3_a5/

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