| Project/Area Number |
23740063
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Tokyo Institute of Technology (2013-2014)
Ritsumeikan University (2011-2012) |
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Principal Investigator |
NITTA Yasufumi 東京工業大学, 理工学研究科, 助教 (90581596)
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | GIT安定性 / 定スカラー曲率ケーラー計量 / 漸近的Chow安定性 / 強K-安定性 / 端的ケーラー計量 / 漸近的相対Chow-Mumford安定性 / 相対強K-安定性 / GIT-安定性 / 相対K-安定性 |
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| Outline of Final Research Achievements |
Firstly, we proved that strong relative K-stability of polarized algebraic manifolds implied asymptotic relative Chow-stability. In particular, as a special case, we see that asymptotic Chow-stability follows from strong K-stability.
Next, we showed the uniqueness of Sasaki-Einstein metrics on compact Sasaki manifolds modulo the action of the identity component of the automorphism group for the transverse holomorphic structure. Also, we obtain a Myers' type theorem for complete Sasaki manifolds with positive transverse Ricci curvature.
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