3-manifolds in Euclidean space from a contact viewpoint (Q987908)

In this paper 3-manifolds \(M\) immersed in \(\mathbb{R}^n\) are studied by using the generalized normal Gauss map \(\Gamma\) on the canal hypersurface \(CM\) and the analysis of the generic singularities of the restrictions of the natural projection \(\eta :CM\rightarrow M\) to different subsets of the singular set of \(\Gamma\). The paper is organized into seven sections as follows: Contacts and singularities; Height functions, binormals and asymptotic directions; Flat geometry and canal hypersurfaces; Generic structure of discriminant sets; Flat ridges; Round geometry on \(3\)-manifolds. Other papers of the second author directly connected to these results are [\textit{M. C. Romero-Fuster}, Proc. R. Soc. Edinb., Sect. A 95, 115--136 (1983; Zbl 0526.58008), Mat. Contemp. 12, 167--182 (1997; Zbl 0939.58036), Proc. R. Soc. Edinb., Sect. A, Math. 132, No.~4, 975--984 (2002; Zbl 1027.53004), Differ. Geom. Appl. 16, No.~3, 213--224 (2002; Zbl 1035.53012) (with \textit{F. Sanchez-Bringas})].