Geometry of the parabolic subset of generically immersed 3-manifolds in \(\mathbb{R}^4\) (Q6546411)

The parabolic subset of a 3-manifold generically immersed in \(\mathbb{R}^4\) is a surface. The authors investigate the generic geometrical behaviour of these surfaces, considered as a submanifold of \(\mathbb{R}^4\). In order to do so, they apply typical singularity theory techniques based on the analysis of the family of height functions. Furthermore, they describe geometrical characterizations of different singularity types.