2015 Fiscal Year Final Research Report
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 |
Section | 一般 |
Research Field |
Geometry
|
Research Institution | Shizuoka University |
Principal Investigator |
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Project Period (FY) |
2012-04-01 – 2016-03-31
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Keywords | 部分多様体 / ラプラス作用素 |
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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Free Research Field |
幾何学
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