Flat Approximations of Surfaces Along Curves
We consider a developable surface tangent to a surface along a curve on the surface. We call it an osculating developable surface along the curve on the surface. We investigate the uniqueness and the singularities of such developable surfaces. We discover two new invariants of curves on a surface wh...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2015-06-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/dema.2015.48.issue-2/dema-2015-0018/dema-2015-0018.xml?format=INT |
| Summary: | We consider a developable surface tangent to a surface along a curve on the surface. We call it an osculating developable surface along the curve on the surface. We investigate the uniqueness and the singularities of such developable surfaces. We discover two new invariants of curves on a surface which characterize these singularities. As a by-product, we show that a curve is a contour generator with respect to an orthogonal projection or a central projection if and only if one of these invariants constantly equal to zero. |
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| ISSN: | 0420-1213 2391-4661 |