Study on geometry of symmetric R-spaces and their submanifolds

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04855
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Tokyo University of Science
• Principal Investigator: Tanaka Makiko Sumi 東京理科大学, 理工学部数学科, 教授 (20255623)
• Co-Investigator(Renkei-kenkyūsha): TASAKI Hiroyuki 筑波大学, 数理物質系, 准教授 (30179684)
• Research Collaborator: Eschenburg Jost-Hinrich ; Quast Peter ; Kimura Taro
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 対称R空間 / 部分多様体 / 対蹠集合 / 外的対称空間

Outline of Final Research Achievements

In collaboration with Jost-Hinrich Eschenburg, we introduced the notion of an extrinsic symmetric subspace of an extrinsic symmetric space and gave a characterisation of extrinsic symmetric subspaces by using Lie triple systems.
In collaboration with Hiroyuki Tasaki, we classified maximal antipodal subgroups of the quotient groups of compact classical Lie groups and determined their great antipodal subgroups and by using them we classified maximal antipodal subgroups of the automorphism groups of compact classical Lie algebras.
In collaboration with Hiroyuki Tasaki and Osami Yasukura we classified maximal antipodal subgroups of compact exceptional Lie group G_2 and classified maximal antipodal sets of compact exceptional symmetric space G_2/SO(4). We gave an explicit description of them by using the realization of G_2 as the automorphism group of the Cayley algebra.

Free Research Field

微分幾何学