2011 Fiscal Year Final Research Report
Conformal Geometry, and Geometry of Einstein Metrics and Exotic Differentiable Structures
| Project/Area Number |
21540097
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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 | Tohoku University (2010-2011)
Tokyo University of Science (2009) |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
KOBAYASHI Osamu 熊本大学, 自然科学研究科, 教授 (10153595)
TONEGAWA Yoshihiro 北海道大学, 理学研究科, 教授 (80296748)
KUMURA Hironori 静岡大学, 理学部, 准教授 (30283336)
YAMADA Sumio 東北大学, 大学院・理学研究科, 准教授 (90396416)
ONO Hajime 東京理科大学, 理工学部, 講師 (70467033)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 微分幾何 / 幾何解析 / 微分トポロジー / 共形幾何 / 山辺不変量 / スカラー曲率 / Einstein計量 / 特異空間 |
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| Research Abstract |
For a closed differentiable manifold M, a differential invariant of M, called the Yamabe invariant of M, is one of fundamental subjects in conformal geometry. The studies of the Yamabe problem on singular spaces and Yamabe constants are also important. The results of this Research Theme are the following :
・Aubin's Lemma for the Yamabe constants of infinite covering spaces.
・Positive Mass Theorem for asymptotically flat spaces with singularities.
・Computations of the orbifold Yamabe invariant.
・Proof that any closed 3-manifold with positive flat conformal structure is Kleinian.
・The solvability of the Yamabe Problem on conic spaces.
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