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New special curves and developable surfaces

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83700

Title: New special curves and developable surfaces
Authors: Izumiya, S. Browse this author
Takeuchi, N. Browse this author
Keywords: Helix
Darboux vector
developable surfaces
singularities
Issue Date: Jul-2002
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 555
Start Page: 1
End Page: 10
Abstract: We define new special curves in Euclidean 3-space which we call slant helices and conical geodesic curves. Those notions are generalizations of the notion of cylin­drical helices. One of the results in this paper gives a classification of special de­velopable surfaces under the condition of the existence of such a special curve as a geodesic. As a result, we consider geometric invariants of space curves. By using these invariants, we can estimate the order of contact with those special curves for general space curves. All arguments in this paper are elementary and classi­cal. However, there have been no papers which have investigated slant helices and conical geodesic curves so far as we know.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69304
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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