2013 Fiscal Year Final Research Report
Interaction of submanifold theory, integrable systems and variational method with a focus on affine differential geometry
| Project/Area Number |
22540070
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Kansai University (2012-2013)
Hitotsubashi University (2010-2011) |
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Principal Investigator |
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | アファイン微分幾何 / 部分多様体論 / 可積分系 / 変分法 |
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| Research Abstract |
We studied flat centroaffine surfaces with non-semisimple Tchebychev operator and showed that if the Pick invariant is constant then it is a centroaffine minimal surfaces described by the Meijer G-function. We also regarded centroaffine minimal surfaces, which is a natural generalization of proper affine spheres centered at the origin, as surfaces in the projective space and classified such surfaces whose associated surfaces are projective minimal.
We also studied surfaces in the complexified sphere parametrized by a complexified orthogonal net. Moreover, we introduced the countably infinite number of presymplectic structures on the space of closed equicentroaffine plane curves and showed that such a space can be described by multi-hamiltoninan system.
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