2005 Fiscal Year Final Research Report Summary
Applied singularity theory to exterior differential systems
| Project/Area Number |
14340020
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | HOKKAIDO UNIVERSITY |
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Principal Investigator |
ISHIKAWA Goo Hokkaido Univ., Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (50176161)
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| Co-Investigator(Kenkyū-buntansha) |
YAMAGUCHI Keizo Hokkaido Univ., Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (00113639)
IZUMIYA Shyuichi Hokkaido Univ., Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (80127422)
ONO Kaoru Hokkaido Univ., Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (20204232)
AKITA Toshiyuki Hokkaido Univ., Grad.School of Sci., Asso.Prof., 大学院・理学研究科, 助教授 (30279252)
OHMOTO Toru Hokkaido Univ., Grad.School of Sci., Asso.Prof., 大学院・理学研究科, 助教授 (20264400)
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| Project Period (FY) |
2002 – 2005
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| Keywords | Monge-Ampere equation / Goursat distribution / singular Legendre submanifolds / coisotropic mapping / symplectic moduli space / singular Legendre knot / mapping space quotient / uni-modal plane curve |
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| Research Abstract |
The following results are obtained : Classification of generic singularities in geometric solutions to Monge-Ampere equations. Clarification of Goursat-Legendre correspondence. Basic investigations on singular Legendre submanifolds, in particular singular Legendre curves. Bifurcation of singularities of developables. Estimate on doubly degenerate submanifolds under projective duality. Introduction of the notion of singular coisotropic mappings. Proof of the localization theorem on the symplectic moduli spaces. Basic study on mapping space quotients. Classification theory of singular Legendre knots. Discovery of new singularities of solutions to Monge-Ampere equations in dimension three. Classification of uni-modal curve singularities and determination of their symplectic moduli spaces. Discovery of remarkable similarity between diffeomorphism classification of plane curve singularities and contactomorphism classification of associated Legendre curve singularities.
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