2021 Fiscal Year Final Research Report
Research of submanifolds in symmetric spaces and their time evolution along various curvature flows
Project/Area Number |
18K03311
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Review Section |
Basic Section 11020:Geometry-related
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Research Institution | Tokyo University of Science |
Principal Investigator |
Koike Naoyuki 東京理科大学, 理学部第一部数学科, 教授 (00281410)
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Project Period (FY) |
2018-04-01 – 2022-03-31
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Keywords | 平均曲率流 / 対称空間 / 等径部分多様体 / 複素等焦部分多様体 / 固有フレッドホルム部分多様体 / ゲージ理論 / カラビ・ヤウ構造 / 特殊ラグランジュ部分多様体 |
Outline of Final Research Achievements |
Main research results in this research subject are as follows. First, we proved the homogeneity theorem for isoparametric submanifolds in a symmetric spaces of non-compact type admitting a reflective focal submanifold by using the complexification and the linearization to an infinite dimensional Hilbert space. Secondly we proved a certain kind of collapsing theorem for the invariant regularized mean curvature flow in a Hilbert space equipped with a certain kind of Hilbert Lie group action and made the theory based to apply the collapsing theorem to the Gauge theory. Thirdly we gave a construction of Calabi-Yau structures on the complexification of a symmetric space of compact type and a construction of special Lagrangian submanifolds in the Calabi-Yau manifold.
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Free Research Field |
微分幾何学
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Academic Significance and Societal Importance of the Research Achievements |
本研究課題における研究成果は,微分幾何学の見地から,ゲージ理論や超対称性理論をはじめとする理論物理学を研究する上で,重要な結果になるのではないかと考えている。特に,研究成果の一つである正則化された平均曲率流の研究をゲージ理論へ応用するために土台となる理論の構築は,今後,注目されるのではないかと考えている。
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