Geometry of pseudo-non-degenerate two-ruled hypersurfaces

TL;DR

This paper explores the geometric properties and singularities of pseudo-non-degenerate two-ruled hypersurfaces in four-dimensional Euclidean space, introducing new characterizations and examining their fundamental properties.

Contribution

It introduces the concept of pseudo-non-degenerate two-ruled hypersurfaces and analyzes their properties and singularities, linking them to curves with Frenet-type frames.

Findings

Characterization of striction curves for these hypersurfaces

Construction of pseudo-non-degenerate hypersurfaces from curves with Frenet frames

Analysis of singularities and properties related to the original curve

Abstract

We investigate the singularities of two-ruled hypersurfaces in the Euclidean four-space. By considering the points that minimize the distance between adjacent rulings, we obtain a characterization the striction curve. We introduce the notion of pseudo-non-degenerate two-ruled hypersurfaces and examine their fundamental properties. We show that two-ruled hypersurfaces constructed from a curve equipped with a Frenet-type frame, via height functions, are pseudo-non-degenerate. Furthermore, we study properties of the original curve through the striction curves and the singularities of pseudo-non-degenerate two-ruled hypersurfaces constructed in this manner.