Project/Area Number  09640141 
Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Geometry

Research Institution  Numazu College of Technology 
Principal Investigator 
MACHIDA Yoshinon Numazu College of Techuotagy, Liberal Arts, Assoc.Professor, 一般科目, 助教授 (90141895)

CoInvestigator(Kenkyūbuntansha) 
KAWADA Hiroyuki Liberal Arts, Assis.Professor, 一般科目, 講師 (00249799)
AIHARA Yoshinori Liberal Arts, Assoc.Professor, 一般科目, 助教授 (60175718)

Project Period (FY) 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥2,300,000 (Direct Cost : ¥2,300,000)
Fiscal Year 1998 : ¥1,000,000 (Direct Cost : ¥1,000,000)
Fiscal Year 1997 : ¥1,300,000 (Direct Cost : ¥1,300,000)

Keywords  twistor theory / geometric structure / Grassmannian structure / selfduality / MongeAmpere equation / Grassmann(グラスマン)構造 / ダブル・ファイバリング / 田中理論 
Research Abstract 
An aspect of the twistor theory is to know the relations and correspondences between different geometric structures defined by a double fibration. 1. Grassmannian structures : It is interesting to study the correspondences between Grassmannian structures of type (n, 2) and projective structures. We showed that. after we defined a tautological distribution on the null plane bundle, the distribution is completely integrable if and only if the structure is halff lat. And then we showed the lifting theorem, the reduction theorem and the twistor theorem on the twistor theory of Grassmannian structures. 2. Selfdual octonian structures : On 8dimensional manifolds with Spin (7) structures, the notion of selfduality is defined. We can construct 12dimensional twistor spaces with fiber S*4. We showed that the structure is selfdual if and only if the twistor space has a semiintegrable quaternion structure. 3. The fundamental solutions of Laplace equations : We studied the twistor integral representation of the fundamental solution of the (complex) Laplace equation on the flat complex spacetime. It is represented by integrating some closed differential form associated with the notion of tree in graph theory. 4. MongeAmpere equations : We defined a remarkable class called decomposable MangeAmpere equations in more than three independent variables. We showed that we can associate to the class the characteristic systems.
