Classification of biharmonic maps and biharmonic submanifolds, and its applications
| Project/Area Number |
15K17542
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Shimane University |
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Principal Investigator |
Maeta Shun 島根大学, 学術研究院理工学系, 講師 (00709644)
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| Project Period (FY) |
2015-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 2重調和写像 / 2重調和部分多様体 / Chen予想 / BMO予想 / 3重調和 / 沈め込み / 2重調和曲面 / 回転面 / アインシュタイン多様体 / 山辺ソリトン / 回転対称 / Cotton tensor / vertical cylinder / totally umbilical / semi-parallel / Yamabe soliton / Ricci soliton / 平均曲率 / 調和写像 / 極小曲面 / 平均曲率一定 / 3重調和写像 / k重調和写像 / 極小部分多様体 / 対称空間 / 定曲率空間 |
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| Outline of Final Research Achievements |
I gave many affirmative partial answers to BMO conjecture that is, any complete biharmonic submanifold M in spheres has constant mean curvature" under the following assumptions: 1. the sectional curvature of M is bounded from above and the mean curvature is bounded from below with some integrability conditions, 2. nowhere zero mean curvature vector, the squared norm of the second fundamental form is bounded from above and some integrability conditions. Furthermore, I and Tomoya Miura showed that any triharmonic Riemannian submersion from a 3-dimensional space form is harmonic.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究ではEells-Sampsonにより導入された調和写像の一般化である2重調和写像，3重調和写像の中でも最も重要な問題であるBalmus-Montaldo-Oniciuc予想とChen's conjectureとその一般化の肯定的部分的解決を与えている。
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Report
(6 results)
Research Products
(14 results)
