$3$-manifolds in Euclidean space from a contact viewpoint
Marı́a del Carmen Romero-Fuster, Ana Claudia Nabarro · Communications in Analysis and Geometry · 2009
We study the geometry of 3-manifolds generically embedded in R n by means of the analysis of the singularities of the distance-squared and height functions on them.We describe the local structure of the discriminant (associated to the distribution of asymptotic directions), the ridges and the flat ridges.