Project/Area Number  10640066 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
Geometry

Research Institution  Tokyo University of Agriculture and Technology 
Principal Investigator 
MASHIMO Katsuya Tokyo University of Agriculture and Technology, Faculty of Technology, Professor, 工学部, 教授 (50157187)

CoInvestigator(Kenkyūbuntansha) 
TOJO Koji Chiba Institute of Technology, Lecturer., 工学部, 講師 (30296313)
IKAWA Osamu Fukushima National College of Technology, Department of General Education, Associate Professor., 助教授 (60249745)
KODA Takashi Toyama University, Faculty of Science, Associate Professor., 理学部, 助教授 (40215273)
HASHIMOTO Hideya Nippon Institute of Technology, Faculty of Technology, Associate Professor., 工学部, 助教授 (60218419)
TASAKI Hiroyuki University of Tsukuba, Department of Mathematics, Associate Professor., 数学系, 助教授 (30179684)

Project Fiscal Year 
1998 – 2000

Project Status 
Completed(Fiscal Year 2000)

Budget Amount *help 
¥3,000,000 (Direct Cost : ¥3,000,000)
Fiscal Year 2000 : ¥600,000 (Direct Cost : ¥600,000)
Fiscal Year 1999 : ¥1,100,000 (Direct Cost : ¥1,100,000)
Fiscal Year 1998 : ¥1,300,000 (Direct Cost : ¥1,300,000)

Keywords  6dimensional sphere / Grassmann Geometry / G_2 / 6次元球面 / グラスマン幾何学 / CR部分多様体 / 全実部分多様体 / コンパクトリー群 / カルタン埋め込み / 安定性 
Research Abstract 
The exceptional simple Lie group G_2 acts naturally on the 6dimensional sphere S^6.Consider the decomposition of the Grassmann bundle G_p(TS^6) of all pdimensional subspaces of tangent space of S^6. For a G_2orbit ν of G_p(TS^6), a submanifold N of S^6 is said to be a νsubmanifold if all of the tangent space of N is contained in ν. We investigated the properties of ν submanifolds. 1. Construction and existence : (1) Case p=2, there exists a νsubmanifold for any G_2orbit ν of G_p(TS^6). (2) Case p=3, the orbit space of G_p(TS^6) is identified with the real projective plane. If a compact νsubmanifold exists ν is contained in a line of the real projective plane. We studied if the tubes over a Jholomorphic curve in the direction of the first (or second) Normal bundle is a νsubmanifold. (3) Case p=4, we constructed many 4dimensional CR submanifolds. But for another orbit ν the existence of νsubmanifold is open. 2. G_2 rigidity of CR submanifols We gave a condition that two CR submanifolds are G_2 congruent and as its application we gave a characterization of CR submanifolds given by K.Sekigawa.
