2017 Fiscal Year Final Research Report
Resonance of affine differential geometry and projective differential geometry from the viewpoint of integrability
| Project/Area Number |
26400075
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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 | Kansai University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | アファイン微分幾何 / 射影微分幾何 / 可積分系 |
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| Outline of Final Research Achievements |
We characterized indefinite projective surfaces developable to affine spheres which admit a lift to the affine space of codimension two satisfying a certain kind of the Einstein condition. We determined nondegenerate centroaffine surfaces whose cubic form is parallel or the traceless part of the cubic form is recurrent with respect to the induced connection. We determined nondegenerate centroaffine ruled surfaces satisfying geometric conditions that the center map is a point or a curve, or a part of the plane through the origin. We characterized proper affine spheres centered at the origin of cohomogeneity one, and classified centroaffine minimal surfaces with constant curvature of cohomegeneity one.
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| Free Research Field |
微分幾何学
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