Study of antipodal sets in symmetric spaces with its extension and application

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540064
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: University of Tsukuba
• Principal Investigator: TASAKI Hiroyuki 筑波大学, 数理物質系, 准教授 (30179684)
• Co-Investigator(Renkei-kenkyūsha): TANAKA Makiko 東京理科大学, 理工学部, 教授 (20255623) ; IKAWA Osamu 京都工芸繊維大学, 工芸科学研究科, 教授 (60249745) ; AKAI Takashi 首都大学東京, 理工学研究科, 准教授 (30381445) ; IRIYEH Hiroshi 東京電機大学, 未来科学部, 准教授 (30385489)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 対称空間 / 対蹠集合 / 実形の交叉 / 複素旗多様体 / 有向実Grassmann多様体 / 対称三対

Outline of Final Research Achievements

We showed a necessary and sufficient condition for the intersection of two real forms in a Hermitian symmetric space of compact type to be discrete and proved that the discrete intersection is an orbit of a Weyl group in a joint work with Makiko Tanaka and Osamu Ikawa. We partly extended these results to two real forms in a complex flag manifold in a joint work with Hiroshi Iriyeh and Takashi Sakai.
We associated antipodal sets in real oriented Grassmann manifolds with certain combinatorial objects and classified antipodal sets in the case where the rank is less than 5.

Free Research Field

微分幾何学