“…The problem of the existence of a totally real embedding of S n in C n was considered by Gromov (see [G1] and [G2, p. 193]), Stout-Zame (see [SZ]), Ahern-Rudin (see [AR]), Forstnerič (see [F1], [F2], [F3]). It has turned out that S n admits a smooth totally real embedding in C n only for n " 3, hence [I,Corollary 2.1] implies, in particular, that M 7 t cannot be real-analytically CR-embedded in C 7 . On the other hand, since S 3 is a totally real submanifold of Q 3 , any realanalytic totally real embedding of S 3 in C 3 (which is known to exist, for instance, by [AR]) extends to a biholomorphic map defined in a neighborhood of S 3 in Q 3 .…”