Twistor theoretic approach for the geometry of non-Riemannian type connection

2015 Fiscal Year Final Research Report

• Project/Area Number: 24740050
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Fukushima University
• Principal Investigator: NAKATA Fuminori 福島大学, 人間発達文化学類, 准教授 (80467034)
• Research Collaborator: KAMADA Hiroyuki 宮城教育大学, 教育学部, 教授 (00249799) ; HASHIMOTO Hideya 名城大学, 理工学部, 教授 (60218419) ; OHASHI Misa 名古屋工業大学, 工学部, 准教授 (70710359) ; MATSUSHITA Yasuo 滋賀県立大学, 名誉教授
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: ツイスター理論 / 不定値計量 / 複素幾何学 / 波動方程式

Outline of Final Research Achievements

The twistor correspondence for circle invariant indefinite Einstein-Weyl structure is established, and its relation with the theory of integral transforms and wave equations are found. Investigation for the twistor correspondence for the twisted Tod-Kamada metric is also progressing.
On the other hand, by the collaboration with several specialists, we start an investigation for G2 geometry, and obtained a remarkable result. That is, we succeeded to characterize a geometric structure of the associative Grassmannian via twistor theory in the G2 geometry. This theory is strongly related to the theory of isoparametric hypersurfaces. Moreover, we succeeded to write down a map clearly which is important in the investigation of the associative Grassmannian.

Free Research Field

微分幾何学