2017 Fiscal Year Final Research Report
Research on surfaces and related differential equations from the view point of singularity theory
| Project/Area Number |
15K04867
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Saitama University |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | 特異点論 |
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| Outline of Final Research Achievements |
The analysis of the contact between a nonsingular surface and the cylinders in the three dimensional Euclidean space was completed satisfactorily. We give the necessary and sufficient conditions for the existence of a cylinder which has A1, A2, A3, A4, A5, D4, D5 contact with a given nonsingular surface. Cylindrical directions is defined as a generatrix of the cylinder which has contact with A >=3. A classification of their singular point is also given. Koenderink's formula show that Gauss curvature equals to the product of curvature of contour
and normal curvature for a give direction. We also show Koenderink-type formulas for singular surface with Whitney umbrella.
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| Free Research Field |
特異点理論
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