2010 Fiscal Year Final Research Report
Differential geometric study of surfaces with singularities
| Project/Area Number |
20740028
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Gifu University |
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Principal Investigator |
SAJI Kentaro Gifu University, 教育学部, 准教授 (70451432)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 特異点 / ルジャンドル特異点 / 波面 / 曲率 / 線織面 |
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| Research Abstract |
I gave criteria for cuspidal lips, cuspidal beaks, cuspidal butterfly, umbilics of singularities fronts. Furthermore, I gave criteria for Mond singularity and higher dimensional singularities of fronts.
As applications of them, I clarified relationships between singularities and differential geometric properties of surfaces. Furthermore, I gave an intrinsic formulation of fronts.
Using this, I gave formulas about numbers of singularities.
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