Riemannian submanifolds and geometry of Laplace operator
| Project/Area Number |
24540073
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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 |
Geometry
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| Research Institution | Shizuoka University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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| Keywords | 部分多様体 / ラプラス作用素 / 平均曲率 / submersion / ラプラス-ベルトラミ作用素 / 固有値 / ラプラシアン / 等長的はめ込み |
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| Outline of Final Research Achievements |
Riemannian submanifolds M may exit from a domain of target manifold, if the norm of the curvature of M and the second fundamental form are sufficiently small compared to the target manifolds. In this respect, I considered the case the target manifolds are Riemannian submersion and extended the results of previous paper. I calculate exit radii from cylinderorical domain using the geometric quantity explicitly. I also consider the relationship possibility of immersion and the eigenvalue of the Laplacian.
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Report
(5 results)
Research Products
(2 results)
