Geometry of solvable Lie groups and submanifold geometry
| Project/Area Number |
20740040
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Hiroshima University |
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Principal Investigator |
TAMARU Hiroshi 広島大学, 大学院・理学研究科, 准教授 (50306982)
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| Project Period (FY) |
2008 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| 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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| Keywords | 対称空間 / 超曲面 / 部分多様体 / 微分幾何 / リー群 / 可解群 / アインシュタイン多様体 / 国際情報交換 |
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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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Report
(6 results)
Research Products
(49 results)
