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

### Raúl Oset Sinha

Universitat de València, Burjassot (Valencia), Spain### Farid Tari

Universidade de São Paulo, São Carlos, Brazil

## Abstract

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.

## Cite this article

Raúl Oset Sinha, Farid Tari, Projections of surfaces in $\mathbb R^4$ to $\mathbb R^3$ and the geometry of their singular images. Rev. Mat. Iberoam. 31 (2015), no. 1, pp. 33–50

DOI 10.4171/RMI/825