| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Research Abstract |
We established a framework for studying left-invariant Riemannian metrics on Lie groups in terms of submanifold geometry. As applications, we have obtained a general procedure to get Milnor-type theorems, and a characterization of algebraic Ricci solitons in terms of submanifold geometry in three-dimensional cases. We have also studied homogeneous submanifolds in noncompact symmetric spaces, and obtained a classification of hyperpolar foliations and a rough classification of cohomogeneity one actions. Results on geometric properties of some particular submanifolds have also been obtained.
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