2011 Fiscal Year Final Research Report
Studies on some open problems concerning flat tori in the unit 3-sphere
| Project/Area Number |
21540066
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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 |
Geometry
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| Research Institution | Utsunomiya University |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2011
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| Keywords | 微分幾何 |
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| Research Abstract |
Diameter conjecture on flat tori in the unit 3-sphere states that the extrinsic diameter of isometrically immersed flat tori in the unit 3-sphere is equal to π. In this research, we proved the conjecture under the assumption that the mean curvature of the immersion is nonnegative or nonpositive. Using this result, we proved that if f is an isometric immersion of a Clifford torus into the unit 3-sphere whose mean curvature is nonnegative or nonpositive, then the immersion f is congruent to the standard embedding of the Clifford torus.
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Research Products
(9 results)
