English

Geometry of pseudo-non-degenerate two-ruled hypersurfaces

Differential Geometry 2026-03-05 v1

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.

Keywords

Cite

@article{arxiv.2603.03382,
  title  = {Geometry of pseudo-non-degenerate two-ruled hypersurfaces},
  author = {Junzhen Li and Kentaro Saji},
  journal= {arXiv preprint arXiv:2603.03382},
  year   = {2026}
}

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19 pages