2001 Fiscal Year Final Research Report Summary
The twistor correspondence between different geometric structures and its application
| Project/Area Number |
11640097
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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 | Numazu National College of Technology |
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Principal Investigator |
MACHIDA Yoshinori Numazu College of Technology, assistant professor, 教養科, 助教授 (90141895)
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| Co-Investigator(Kenkyū-buntansha) |
FUJII Kazuyuki Yokohama City University, the fealty ofscience, professor, 理学部, 教授 (00128084)
SATO Hajime Nagoya University, Graduate School of Mathemetic, professor, 大学院・多元数理科学研究科, 教授 (30011612)
KAMADA Hiroyuki Numazucollege of Technology, Division of Liberal Arts, assistant porfessor, 教養科, 助教授 (00249799)
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| Project Period (FY) |
1999 – 2001
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| Keywords | twistor theory / pure spinor structure / Language structure / sub-Laplacian / Goursat equation / hypergeometric equation / half-flat pertial connection |
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| Research Abstract |
An aspect of the twistor theory is to see a relation between different geometric structures defined by a double fibration.
1. (1) A pure spinor structure has the model space of the orthonormal frame bundle of the unit sphere. Considering the null plane bundle, we can define the twistor space, which has a neutral conformal structure. 1. (2) A Lagrangian structure has the model space of the Lagrangian Grassmann manifold. Considering the null plane bundle, we can define the twistor space, which has a projective contact structure.
2. (1) We consider twistor integral representations of solutions of the sub-Laplacian defined on a space equipped with a contact structure. The twistor space is all the null spaces associated with a Heisenberg group, 2. (2) Restricting Goursat equations to finite type, we consider local equivalence problems in terms of curvatures of normal Cartan connections.
3. (1) We consider flag manifolds of second kind by various double fiberings defined from a vector space equipped with an inner product or a symplectic form. We generalize the system of hypergeometric equations associated with geometric structures. 3. (2) We consider generalized instantons of gauge fields (half-flat partial connections) on non-holonomic systems (non-integrable distributions).
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