Project/Area Number  11440024 
Research Category 
GrantinAid for Scientific Research (B)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Geometry

Research Institution  TOKYO METROPOLITAN UNIVERSITY 
Principal Investigator 
OGIUE Koichi GRADUATE SCHOOL OF SCIENCE, DEPARTMENT OF MATHEMATICS, PROFESSOR, 理学研究科, 教授 (10087025)

CoInvestigator(Kenkyūbuntansha) 
KOISO Miyuki DEPARTMENT OF MATHEMATICS, KYOTO UNIVERSITY OF EDUCATION, ASSOCIATE PROFESSOR, 教育学部, 助教授 (10178189)
MAEDA Sadahiro DEPARTMENT OF MATHEMATICS, SHIMANE UNIVERSITY, PROFESSOR, 総合理工学部, 教授 (40181581)
OHNITA Yoshihiro GRADUATE SCHOOL OF SCIENCE, DEPARTMENT OF MATHEMATICS, PROFESSOR, 理学研究科, 教授 (90183764)
MIYAOKA Reiko DEPARTMENT OF MATHEMATICS, SOPHIA UNIVERSITY, PROFESSOR, 理工学部, 教授 (70108182)
HAMADA Tatsuyoshi DEPARTMENT OF APPLIED MATHEMATICS, FACULTY OF SCIENCE, FUKUOKA UNIVERSITY, RESEARCH ASSOCIATE, 理学部, 助手 (90299537)
北川 義久 宇都宮大学, 教育学部, 助教授 (20144917)
神島 芳宣 東京都立大学, 大学院・理学研究科, 教授 (10125304)
山田 光太郎 九州大学, 大学院・数理学研究科, 教授 (10221657)
剱持 勝衛 東北大学, 大学院・理学研究科, 教授 (60004404)

Project Period (FY) 
1999 – 2001

Project Status 
Completed(Fiscal Year 2001)

Budget Amount *help 
¥15,100,000 (Direct Cost : ¥15,100,000)
Fiscal Year 2001 : ¥1,500,000 (Direct Cost : ¥1,500,000)
Fiscal Year 2000 : ¥6,100,000 (Direct Cost : ¥6,100,000)
Fiscal Year 1999 : ¥7,500,000 (Direct Cost : ¥7,500,000)

Keywords  Submanifold / Differential Geometry / Curve / Surface / Curvature / Riemannian manifold / Geometric structure 
Research Abstract 
In this project, we had several sizes of symposium, international conferences, workshops etc. 3 times in 1999, 3 times in 2000, 2 times in 2001. Especially, we organized the 46th Geometry Symposium at Univ. of Tokyo in August, 1999, the 9th MSJIRI " Integrable Systems in Differential Geometry " in July, 2000, and an international workshop on Geometry of Riemannian Submanifolds at Tokyo Metropolitan Univ. in December, 2001. There we were able to have talks of results, discussions and interchanges of informations about differential geometric research on submanifolds synthetically and to receive the review for this project. Ogiue, Maeda, Adachi developed study of curves, in particular circles, in more general symmetric spaces and their submanifolds than complex space forms, and obtain the results. Especially their research examining in details the length spectrum of geodesic spheres in complex space froms by the number theoretic method were highly estimated and published in J. Math. Soc
… More
. Japan. Miyaoka gave a different proof of homogeneity for the case six principal curvatures and multiplicity 1 in the classification problem of isoparametric hypersurafces and her work got the high estimate. Further in cooperation with Ishikawa, and Kimura, she constructed many compact submanifolds in spheres with degenerate Gauss maps satisfying the equality of Ferus and gave many examples of special Lagrangian submanifolds as a byproduct. Kitagawa studied isometric deformations of flat tori in 3dimensional standard sphere with nonconstant mean curvature and proved that these flat tori are all deformable. Kenmotsu classified parallel mean curvature surfaces with constant Gaussian curvature in complex space forms by analyzing precisely a certain nonlinear ordinary differential equation and his work was decided to be published in an internationally high journal. In joint works with Hashimoto and Mashimo, Sekigawa gave the structure equations for 4dimensional CRsubmanifolds in the nearly K\"ahler 6dimensional sphere by the moving frame method in Bryant's style, and as applications he studied fundamental properties of characteristic classes of such submanifolds and provided new examples by the Lie theoretic method. Koiso analyzed actively deformation and stability problem of constant mean curvature surfaces with boundary and obtained excellent results. On the other hand, Ogiue, Nakamula, Hamada greatly have maken good use of the system (PPDG) interchanging extensively and effectively research results and informations, and we expect that this system will be developed to the Geometry Server in future by Guest and Ohnita. Less
