2021 Fiscal Year Final Research Report
A variational problem on conformality of maps and a variational problem on pullbacks of metrics
| Project/Area Number |
18K03280
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 11020:Geometry-related
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| Research Institution | Yamaguchi University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
内藤 博夫 山口大学, その他部局等, 名誉教授 (10127772)
近藤 慶 岡山大学, 自然科学研究科, 教授 (70736123)
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| Project Period (FY) |
2018-04-01 – 2022-03-31
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| Keywords | variational problem / symphonic map / C-stationary map / pullback / Riemannian manifold |
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| Outline of Final Research Achievements |
A "manifold", or in particular "Riemannian manifold" is a general concept of "a (curved) space", and a "map" between manifolds gives a "relation" between them. The researcher in this research project introduced two new concepts "C-stationary maps" and "symphonic maps" for maps between Riemannian manifolds. In this project we give some new steps and results on these two concepts.
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| Free Research Field |
differential geometry
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| Academic Significance and Societal Importance of the Research Achievements |
これらの新しい概念は, もともと「共形写像」という重要な概念から導かれたものであり, 本研究課題の研究成果は, 「共形写像」を含む問題への応用を念頭に置いている. また, 本研究の過程で用いられる議論や手法が, 幾何解析 (Geometric Analysis) の他の分野へ影響を与えることも期待している.
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