| Co-Investigator(Kenkyū-buntansha) |
MAEDA Sadahiro DEPARTMENT OF MATHEMATICS, SHIMANE UNIVERSITY, PROFESSOR, 総合理工学部, 教授 (40181581)
NAKAMULA Ken FACULTY OF SCIENCE, DEPARTMENT OF MATHEMATICS, TOKYO METROPOLITAN UNIVERSITY, PROFESSOR, 大学院・理学研究科, 教授 (80110849)
OHNITA Yoshihiro GRADUATE SCHOOL OF SCIENCE, DEPARTMENT OF MATHEMATICS, TOKYO METROPOLITAN UNIVERSITY, PROFESSOR, 大学院・理学研究科, 教授 (90183764)
KENMOTSU Katsuei MATHEMATICAL INSTITUTE, TOHOKU UNIVERSITY, PROFESSOR, 理学研究科, 教授 (60004404)
UDAGAWA Seiichi DEPARTMENT OF MATHEMATICS, SCHOOL OF MEDICINE, NIHON UNIVERSITY, LECTURER, 医学部, 講師 (70193878)
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| Research Abstract |
Differential Geometry is originated to the study of curves and surfaces in 3-dimensional Euclidian space and submanifold theory is a central research subject. One of this research project is to develop the differential geometric research of submanifolds and the study of its realted branches. Another is to construct and to work the systems for the effective dissemination of research in this field. In 1997, after the head investigator and investigators discussed working plans and made a setting of research aims and a choice of priority items in each division of project, and organized research groups led by each investigators, we started the research activities. First, in order to enable us effective exchange of informations, Nakamula and Hamada led to construct a mailing system and to start a use of the system. At present, 246 researchers of this area in the world belong to the system. In order to report research results in the environs of each investigators and to obtain informations fr
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om neighboring areas, we organized 4 conferences in 1997 and 4 conferences in 1998. They are extremely important on step up our research. Especially conferences inviting foreign researchers had much effect on enlarging our view. It was very advantageous that investigators joined international conferences outside the country and gave talks on their research results, and they were able to have information exchange with many foreign mathematicians. As results of these activities, Ogiue, Maeda, Adachi, Udagawa and others greatly contributed to give so many results in the study of curves (closed geodesics, circles, helixes) in specific Riemanninan manifolds and their submanifolds. Concerned with the study of surfaces and real hypersurfaces in spheres and complex projective spaces, Maeda, Takagi, Kitagawa and others provided many deep results. Strikingly, Miyaoka provided a wonderful progress in the classification problem since E. Cartan of isoparametric hypersurfaces in spheres, and Kenmotsu provided a big progress in the classification problem since E. Cartan of minimal surfaces with constant Gaussian curvature in complex projective spaces beginning from S.S. Chern's work. In the study of harmonic maps of Riemann surfaces into symmetric spaces and their realted minimal surfaces, Ejiri, Ohnita, Udagawa and others gaves several progress from the viewpoint of theory of integrable systems. From the viewpoint of singularity theory, knot theory, gauge theory, moduli spaces etc. and other neighboring branches, Izumiya, Ohara, Ohnita and others worked on this research project and gave new results. Based on these results of this project, we greatly expect the further progress of this area. Less
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