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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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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