Revista Matemática Iberoamericana


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Volume 31, Issue 1, 2015, pp. 33–50
DOI: 10.4171/RMI/825

Published online: 2015-03-05

Projections of surfaces in $\mathbb R^4$ to $\mathbb R^3$ and the geometry of their singular images

Raúl Oset Sinha[1] and Farid Tari[2]

(1) Universitat de València, Burjassot (Valencia), Spain
(2) Universidade de São Paulo, São Carlos, Brazil

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

Keywords: Projections, singular surfaces in $\mathbb R^3$, surfaces in $\mathbb R^4$

Oset Sinha Raúl, Tari Farid: Projections of surfaces in $\mathbb R^4$ to $\mathbb R^3$ and the geometry of their singular images. Rev. Mat. Iberoamericana 31 (2015), 33-50. doi: 10.4171/RMI/825