Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >
New special curves and developable surfaces
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 |
Publisher: | Department of Mathematics, Hokkaido University |
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
|