| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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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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