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We describe the real forms of Gizatullin surfaces of the form $xy=p(z)$ andof Koras-Russell threefolds of the first kind. The former admit zero, two,three, four or six isomorphism classes of real forms, depending on the degreeand the symmetries of the polynomial~$p$. The latter, which are threefoldsgiven by an equation of the form $x^dy+z^k+x+t^\ell=0$, all admit exactly onereal form up to isomorphism.

Real forms of some Gizatullin surfaces and Koras-Russell threefolds