2021-01-28T09:51:30Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/796072020-10-22T05:31:33Zhdl_2115_20039hdl_2115_116GEOMETRIC ALGEBRA AND SINGULARITIES OF RULED AND DEVELOPABLE SURFACESTanaka, JunkiOhmoto, ToruDifferential line geometryClifford algebraRuled surfacesDevelopable surfacesSingularities of smooth maps413Any 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.Worldwide Center of MathematicsJournal Articlehttp://hdl.handle.net/2115/796071949-2006Journal of Singularities212492672020-10-22enginfo:doi/10.5427/jsing.2020.21onone