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# Wydawnictwa / Banach Center Publications / Wszystkie tomy

## Singularities of non-degenerate $n$-ruled $(n+1)$-manifolds in Euclidean space

### Tom 65 / 2004

Banach Center Publications 65 (2004), 211-225 MSC: Primary 57R45; Secondary 53A25, 53A07. DOI: 10.4064/bc65-0-14

#### Streszczenie

The objective of this paper is to study singularities of $n$-ruled $(n+1)$-manifolds in Euclidean space. They are one-parameter families of $n$-dimensional affine subspaces in Euclidean space. After defining a non-degenerate $n$-ruled $(n+1)$-manifold we will give a necessary and sufficient condition for such a map germ to be right-left equivalent to the cross cap $\times$ interval. The behavior of a generic $n$-ruled $(n+1)$-manifold is also discussed.

#### Autorzy

• Kentaro SajiDepartment of Mathematics