Development of Theory of Harmonic Maps
| Project/Area Number |
25400154
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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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| Research Field |
Mathematical analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
Urakawa Hajime 東北大学, 高度教養教育・学生支援機構, 名誉教授 (50022679)
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | エネルギー汎関数 / ２－調和写像 / 調和写像 / ２－エネルギー汎関数 / 対称空間 / ２－調和部分多様体 / 葉層多様体 / コーシー・リーマン多様体 / G－主束 / ねじれ束 / ハーマン作用 / 軌道 / 多重調和写像 / ユークリッド空間 / リーマン多様体 / 極小 / 埋め込み / 主曲率 / リー群 / エネルギー / ２－エネルギー / バブリング現象 / m-エネルギー / 非正曲率 / 強擬凸リーマン多様体 / チェン予想 / CR類比 / テンション場 / k-調和写像 / コンパクト・リー群 |
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| Outline of Final Research Achievements |
Harmonic map is a critical point of the energy and biharmonic map is the one of the 2-energy. Both theories have been developed greatly in the world. We have clarified the similarities and differences between these theories, recently. We have constructed several examples of biharmonic maps which are not harmonic maps. We gave and clarified the conditions which biharmonic maps must be harmonic maps.
We have constructed and classified all homogeneous biharmonic submanifolds in the symmetric space which are not harmonic.
We gave the similar notions of biharmonic foliations and also pseudo biharmonic submanifolds in Cauchy-Riemannian geometry, and gave several such examples.
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Report
(6 results)
Research Products
(67 results)
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[Presentation] ２重調和部分多様体2014
Author(s)
浦川 肇, 小磯憲史
Organizer
日本数学会, 幾何学分科会
Place of Presentation
広島大学
Year and Date
2014-09-25 – 2014-09-27
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[Book] 微分積分学第２巻2017
Author(s)
藤原松三郎、浦川肇、高木泉、藤原毅夫
Total Pages
634
Publisher
内田老鶴圃
ISBN
9784753601646
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