2010 Fiscal Year Final Research Report
The symmetry and the homogeneity in pseudo-Riemannian geometry
| Project/Area Number |
20540067
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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 | Ochanomizu University |
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Principal Investigator |
TSUKADA Kazumi Ochanomizu University, 大学院・人間文化創成科学研究科, 教授 (30163760)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 無限小等質空間 / 共形平坦等質ローレンツ多様体 / ホロ円曲面 |
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| Research Abstract |
We studied the following subjects on the symmetry and the homogeneity in pseudo-Riemannian geometry .We developed the classification problem of conformally flat homogeneous Lorentzian manifolds. For almost all types of the Ricci operators, we have solved the construction and the classification problem. We construct horocyclic surfaces in hyperbolic3-space associated with spacelike curves in the lightcone and classify their singularities using invariants of corresponding spacelike curves.
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