1998 Fiscal Year Final Research Report Summary
Surfaces with parallel mean curvature vector in Complex projective spaces
| Project/Area Number |
09640085
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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 | Yamagata U. |
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Principal Investigator |
OGATA Takashi Faculty of Science, Prof., 理学部, 教授 (10042425)
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| Co-Investigator(Kenkyū-buntansha) |
UCHIDA Yoshiaki Faculty of Science, Aso.Prof., 理学部, 助教授 (80280890)
SAWADA Hideki Faculty of Science, Aso.Prof., 理学部, 助教授 (30095856)
II Kiyotaka Faculty of Science, Aso.Prof., 理学部, 助教授 (10007180)
HIRABUKI Shinkichi Faculty of Science, Aso.Prof., 理学部, 助教授 (70007136)
OHIKE Hiroshi Faculty of Science, Prof., 理学部, 教授 (20007165)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Kaehler angle / minimal surface / complex projective space / cryptology / knot theory / Carnot space / tangent bundle / quaternion projective space |
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| Research Abstract |
The purpose of our research is to investigate properties of the complex projective space from several points of view using various kinds of method. Each investigator has aimed to develop the research using his own special knowledge and have the following research results.
Ogata, the head of this investigating team, has studied characterization and classification of surfaces with parallel mean curvature vector field in the complex projective space and proved that there exist minimal surfaces with constant Kaehler angle and non-constant Gaussian curvature in the 2-dimensional complex projective space.
Hirabuki has proved Krull-Akizuki theorem for semigroups by using the method of proving theorem for rings arising from semigroup rings.
It has constructed complex structures on the tangent bundle of the quaternion projective space by using the geometrical technique and proved that these complex structures correspond with the ones which were given by Furuya-Tanaka-Yoshizawa.
Sawada has algebrically described cryptology and considered it as a group action. Specially he has examined the structure of groups related to RSA cryptosystems and showed the existence of a pair of different keys which encrypt messages equally. These results are read at the 20-th civil lecture promoted by Japan Mathematical Society,
Uchida has proved that many periodical knots have not the DELTA-unknotting number 1. Moreover, he conjecture that the periodical unknotting number is not 1 for the usual unknotting operation.
Ueno has studied the Dirichlet problems at infinity for harmonic maps between the Carnot spaces. The obtained results are read at the research meetings held at Tokyo Metropolitan Univ. and Yamaguchi Univ..
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