Studies on left-invariant geometric structures by submanifold theory

2018 Fiscal Year Final Research Report

• Project/Area Number: 26287012
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Osaka City University (2018); Hiroshima University (2014-2017)
• Principal Investigator: Tamaru Hiroshi 大阪市立大学, 大学院理学研究科, 教授 (50306982)
• Co-Investigator(Kenkyū-buntansha): 澁谷 一博 広島大学, 理学研究科, 准教授 (00569832) ; 奥田 隆幸 広島大学, 理学研究科, 講師 (40725131) ; 阿賀岡 芳夫 広島大学, 理学研究科, 教授 (50192894)
• Project Period (FY): 2014-04-01 – 2019-03-31
• Keywords: 対称空間 / 部分多様体 / リー群 / 左不変計量 / 幾何構造

Outline of Final Research Achievements

We have had progresses on submanifold geometry of symmetric spaces, left-invariant geometric structures, and their fusional studies. In particular, for left-invariant Riemannin metrics, several papers which construct the basic of our study have been published. Moreover, we also constructed similar frameworks for other left-invariant geometric structures, described the moduli space of left-invariant Lorentzian metrics on some particular nilpotent Lie groups, and establish a method to examine the existence and nonexistence of left-invariant symplectic structures on a given Lie group.

Free Research Field

幾何学

Academic Significance and Societal Importance of the Research Achievements

左不変な幾何構造と部分多様体論を繋ぐ研究は我々の独自のものであり，そのような研究を創出することは学術的な意義をもつもとだと考える。特に，新しい分野において新しい問題を提出したことは，今後の数学の発展にも寄与するものと考える。