Infinitely transitive actions on real affine suspensions

A group G acts infinitely transitively on a set Y if for every positive integer m, its action is m-transitive on Y. Given a real affine algebraic variety Y of dimension greater than or equal to 2, we show that, under a mild restriction, if the special automorphism group of Y (the group generated by one-parameter unipotent subgroups) is infinitely transitive on each connected component of the smooth locus , then for any real affine suspension X over Y, the special automorphism group of X is infinitely transitive on each connected component of . This generalizes a recent result given by Arzhantsev, Kuyumzhiyan, and Zaidenberg over the field of real numbers.