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On cylindrical directions of regular surfaces in ℝ4 derived from contact with spherical cylinders
Abstract
We investigate the contact of regular surfaces in ℝ4 with spherical cylinders S2(r) × ℝ. We introduce cylindrical directions of these surfaces, defined by the axes of spherical cylinders having degenerate contact with the surfaces, and show that these directions capture the ridge condition of projected regular surfaces under orthogonal projection along these directions.
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BibTeX
@misc{hasegawa2026cylindrical,
title = {{On cylindrical directions of regular surfaces in $\mathbbR^4$ derived from contact with spherical cylinders}},
author = {Masaru Hasegawa},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01912},
eprint = {2611.01912},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01912},
}
RIS
TY - UNPB
TI - On cylindrical directions of regular surfaces in ℝ^4 derived from contact with spherical cylinders
AU - Masaru Hasegawa
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01912
UR - https://arxiv.org/abs/2611.01912
AB - We investigate the contact of regular surfaces in ℝ^4 with spherical cylinders S^2(r) × ℝ. We introduce cylindrical directions of these surfaces, defined by the axes of spherical cylinders having degenerate contact with the surfaces, and show that these directions capture the ridge condition of projected regular surfaces under orthogonal projection along these directions.
ER -