On surfaces and their contours

Abstract

We prove two theorems concerning the global behaviour of a smooth compact surface S, without boundary, embedded in a real projective space or mapped to a plane. Our starting point is an analysis of the orientability properties of the normal bundle of a singular projective curve. Then we see how an excellent projection from S to the Euclidean plane gives rise to integral relations linking the singularities of the apparent contour. Finally, given an embedding of S in RPn, we look at the discriminant Δ* of a net of hyperplanes that intersects S in a generic way, obtaining a characterization of Δ* in terms of mod.2 cohomology invariants. © 1991 Springer-Verlag.