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Geometry on curves which go around a Whitney umbrella

Differential Geometry 2025-08-22 v1

Abstract

We consider curves which go around Whitney umbrella. Then we consider the geodesic and the normal curvatures, ruled surfaces generated by the normal vector and normal developable surfaces with respect to the tangent and bi-tangent vectors of the curve. Then we obtain several functions which represents geometry on Whitney umbrella. Looking at the top terms of them with respect to the radius, we study geometry on Whitney umbrella.

Keywords

Cite

@article{arxiv.2508.15293,
  title  = {Geometry on curves which go around a Whitney umbrella},
  author = {Masayuki Hara},
  journal= {arXiv preprint arXiv:2508.15293},
  year   = {2025}
}

Comments

12 pages, 3 figures