Abstract
In this project we propose to investigate corank $1$ singular surfaces in $\mathbb{R}^4$ from several points of view: associating it with the geometry of space curves, singular $3$-manifolds in $\mathbb{R}^5$ and projections into singular surfaces in $\mathbb{R}^3$. Moreover, we aim to extend the study to corank $1$ surfaces in $\mathbb{R}^n$, $n>4$.