2010 Fiscal Year Final Research Report
Research of surfaces in four-dimensional Riemannian manifolds using their twistor lifts
| Project/Area Number |
20740046
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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 | Kanazawa University (2009-2011)
Tokyo University of Science (2008) |
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Principal Investigator |
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| Project Period (FY) |
2008 – 2010
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| Keywords | ツイスター空間 / ツイスターリフト / 調和切断 |
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| Research Abstract |
We classify surfaces of genus zero in self-dual Einstein manifolds whose twistor lifts are harmonic sections. Using this result, we obtain a classification for the quotient space of the space of all twistor holomorphis surfaces by conformal transformations in the special case. Moreover we show that twsitor lifts of twistor holomorphic surfaces are weakly stable as harmonic sections if ambient spaces are self-dual Einstein manifolds of non-negative scalar curvature. Conversely, if the ambient space is Euclidean space, a surface whose twistor lift is a weakly stable harmonic section is twistor holomorphic.
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