| 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)
諏訪 立雄 北海道大学, 大学院・理学研究科, 教授 (40109418)
宮岡 礼子 九州大学, 理学部, 教授 (70108182)
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| Project Period (FY) |
2002 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥11,900,000 (Direct Cost: ¥11,900,000)
Fiscal Year 2005: ¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2004: ¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 2003: ¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 2002: ¥3,700,000 (Direct Cost: ¥3,700,000)
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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 / ガウス・クロネッカー曲率 / 接触モデュライ空間 / ユニモダル特異点 / モンジュ・アンペール系 / アイソトロピック写像 / 特異ラグランジュ多様体 / グルサ系 / ガウス曲率 / 非固有アフィン曲面 / ルジャンドル曲線 / 微分構造 / サーストン・ベネカン不変量 / マスロフ不変量 / 非正規型常微分方程式 / 解空間零点定理 |
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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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