[K2] N.H. Kuiper, Convex immersions of closed surfaces in E^3, Comm. Math. Helv. 35 (1961) 85-92.This paper deals specifically with immersions into three-space, and gives a good description of tightness. It gives the decomposition of a tight surface into the M+ and M- regions . It shows that the real projective plane and the Klein bottle do not admit tight immersions into three-space, and that any other surface (except the one with Euler characteristic -1) can be tightly immersed.
This paper describes an immersion of the real projective plane with exactly one minimum, one maximum and one saddle point, and it points out how this could be used to produce an eversion of the sphere.
10/12/94 firstname.lastname@example.org --
The Geometry Center