Projections of surfaces in 'R POT.4' to 'R POT.3' and the geometry of their singular images

Abstract

We study the geometry of germs of singular surfaces in 'R POT.3' whose parametrisations have an A-singularity of 'A IND.E'-codimension less than or equal to 3, via their contact with planes. These singular surfaces occur as projections of smooth surfaces in 'R POT.4' to 'R POT.3'. We recover some aspects of the extrinsic geometry of these surfaces in 'R POT.4' from those of the images of their projections.