Symmetric models of the real projective plane (Q1591727)

The authors make an interesting study of the symmetry group of a stable immersion of the real projective plane in Euclidean 3-space. They show that this symmetry group is either trivial or is cyclic of order 3. They also show that the symmetry group of a stable map of the real projective plane in Euclidean 3-space is conjugate to a subgroup of the full tetrahedral group. From these results they conclude that the best-known stable immersion of this kind, namely Boy's surface, is the most symmetrical one, and that Steiner's surface (also called the Roman surface) is given by the most symmetrical stable map of this kind. Finally, the authors construct a smooth embedding of the real projective plane into 4-dimensional Euclidean space with the circle group as symmetry group by orthogonal projection of the Veronese surface.