2017 Fiscal Year Final Research Report
Deepening singularity theory and low dimensional geometry
Project/Area Number |
26400087
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Geometry
|
Research Institution | Kobe University |
Principal Investigator |
Saji Kentaro 神戸大学, 理学研究科, 准教授 (70451432)
|
Project Period (FY) |
2014-04-01 – 2018-03-31
|
Keywords | 特異点 / カスプ辺 / 接触構造 / 曲率 |
Outline of Final Research Achievements |
For deepening singularity theory, I obtained criteria for Morin singularities for the case of the dimension of the source space and the target space is not the same. By using criteria for Morin singularities, I gave the number of right-left isotopy classes. For low dimensional geometry, I generalized a formula for the number of singular points and the Euler characteristic to singularities of bundle homomorphisms. I also gave a normal form by only using isometric coordinate transformation of the target space for cuspidal edges and swallowtails. Moreover, I clarified the differential geometric meanings for modulus appeared in the lower degree terms. By using that form, I obtained generic configurations of asymptotic lines and characteristic lines of that singularities. I also studied singularities of solution surfaces of certain differential equation and that of surfaces which approximate the cuspidal edge.
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Free Research Field |
微分トポロジー
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