2012 Fiscal Year Final Research Report
New development of harmonic maps
| Project/Area Number |
21540207
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
ICHIYAMA Toshiyuki 亜細亜大学, 経済学部, 教授 (70213014)
ITOH Jinichi 熊本大学, 教育学部, 教授 (20193493)
OBATA Nobuaki 東北大学, 大学院・情報科学研究科 (10169360)
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| Co-Investigator(Renkei-kenkyūsha) |
INOGUCHI Junichi 山形大学, 理学部, 准教授 (40309886)
HIAI Fumio 東北大学, 大学院・情報科学研究科, 教授 (30092571)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 調和写像 / 2-調和写像 / 2-ヤング・ミルズ場 / 非正曲率 / コンパクト・リー群 |
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| Research Abstract |
In 1986, the concept of the bi-harmonic map which is an extension of harmonic maps was introduced. We raised the new notion of the bi-Yang-Mills field, which is an analog of the bi-harmonic map, and showed its isolation phenomena. That is, bi-Yang-Mills fields with some square-integral norm over compact manifolds with positive Ricci curvature must be Yang-Mills fields. We showed bi-harmonic maps which have a bounded square-integral norm must be harmonic if the target space has non-positive curvature. We classified all the bi-harmonic maps for cases where the target space is a compact Lie group or compact symmetric spaces.
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