2011 Fiscal Year Final Research Report
Research on variational problems associated with higher order geometric structures
| Project/Area Number |
20340009
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 |
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Principal Investigator |
NISHIKAWA Seiki 東北大学, 大学院・理学研究科, 名誉教授 (60004488)
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| Project Period (FY) |
2008 – 2011
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| Keywords | 調和写像 / エネルギー汎関数 / 複素フィンスラー計量 / 全Q曲率 / 高次の幾何構 造 / 変分問題 |
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| Research Abstract |
Through a multidisciplinary research on variational problems associated with higher order geometric structures, such as Finsler structures and conformal structures, we prove the following. 1) Any energy minimizing harmonic map from the Riemann sphere into a weakly Kaehler Finsler manifold of positive curvature is either holomorphic or antiholomorphic. 2) The singular set of a nonholomorphic harmonic map from a compact Riemann surface into a complex Finsler manifold is a finite set. 3) Under volume preserving conformal variations of metrics, each Einstein metric of positive scalar curvature is a stable critical point of the total Q curvature.
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