Abstract
We investigate differential geometric properties of a parabolic point of a surface in the Euclidean three space. We introduce the contact cylindrical surface which is a cylindrical surface having a degenerate contact type with the original surface at a parabolic point. Furthermore, we show that such a contact property gives a characterization to the \(\mathcal {A}\)-singularity of the orthogonal projection of a surface from the asymptotic direction.
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Acknowledgements
The authors would like to thank the referee for helpful comments to improve the original manuscript. The authors also thank Toshizumi Fukui and Farid Tari for helpful discussions. This work is partially supported by JSPS KAKENHI Grant numbers 21K03230, 20K14312, 18K03301, Japan-Brazil bilateral project JPJSBP1 20190103 and Japan-Russia Research Cooperative Program 120194801.
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Hasegawa, M., Kabata, Y. & Saji, K. Contact Cylindrical Surfaces and a Projection of a Surface Around a Parabolic Point. Arnold Math J. (2024). https://doi.org/10.1007/s40598-024-00251-y
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DOI: https://doi.org/10.1007/s40598-024-00251-y