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Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Peer-reviewed Journal Articles, etc >
GEOMETRIC ALGEBRA AND SINGULARITIES OF RULED AND DEVELOPABLE SURFACES
| Title: | GEOMETRIC ALGEBRA AND SINGULARITIES OF RULED AND DEVELOPABLE SURFACES |
| Authors: | Tanaka, Junki Browse this author | | Ohmoto, Toru Browse this author |
| Keywords: | Differential line geometry | | Clifford algebra | | Ruled surfaces | | Developable surfaces | | Singularities of smooth maps |
| Issue Date: | 22-Oct-2020 |
| Publisher: | Worldwide Center of Mathematics |
| Journal Title: | Journal of Singularities |
| Volume: | 21 |
| Start Page: | 249 |
| End Page: | 267 |
| Publisher DOI: | 10.5427/jsing.2020.21o |
| Abstract: | Any ruled surface in R-3 is described as a curve of unit dual vectors in the algebra of dual quaternions (=the even Clifford algebra Cl+ (0, 3, 1)). Combining this classical framework and A-classification theory of C-infinity map-germs (R-2, 0) -> (R-3, 0), we characterize local diffeomorphic types of singular ruled surfaces in terms of geometric invariants. In particular, using a theorem of G. Ishikawa, we show that local topological type of singular developable surfaces is completely determined by vanishing order of the dual torsion tau, that generalizes an old result of D. Mond for tangent developables of non-singular space curves. This work suggests that Geometric Algebra would be useful for studying singularities of geometric objects in classical Klein geometries. |
| Type: | article |
| URI: | http://hdl.handle.net/2115/79607 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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