2013 Fiscal Year Final Research Report
Research on geometries of Differential Systems and Parabolic geometries
| Project/Area Number |
23540065
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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 | Hokkaido University |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| Keywords | 接触幾何学 / 微分式系 / 階別単純リー環 / 包合系 |
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| Research Abstract |
We established the notion of PD-manifolds, which describes, through the concept of differentail systems, the geometry of systems of second order partial differential equations for one unknown function under contact transformations. Moerover we established two step Reduction Theorem, which is basic to Contact Geometry of Second Order.
By utilizing this Reduction Theorem, we explicitly show how to construct various classes of overdetermined systems of second order partial differential equations, for which the contact equivalence problems are reduced to that of Parabolic Geometries(i.e., the geometries associated with the simple graded Lie algebras).
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Research Products
(6 results)
