2004 Fiscal Year Final Research Report Summary
Combinatorial structures on Riemann surfaces and topological properties of the moduli space.
| Project/Area Number |
14540068
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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 |
OHBA Kiyoshi Ochanomizu University, Faculty of Science, associate professor, 理学部, 助手 (80242337)
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| Co-Investigator(Kenkyū-buntansha) |
YOKOGAWA Koji Ochanomizu University, Faculty of Science, professor, 大学院・人間文化研究科, 教授 (40240189)
HASHIMOTO Yoshitake Osaka City University, Graduate School of Science, associate professor, 大学院・理学研究科, 助教授 (20271182)
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| Project Period (FY) |
2002 – 2004
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| Keywords | Riemann surface / Abelian differential / combinatorial structure / genus / Haefliger knot |
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| Research Abstract |
Our results are as follows :
1.We consider Riemann surfaces with Abelian differential constructed from lightning pairs. A lightning pair is a pieacewise linear loop in the complex plane determined by a certain kind of combinatorial data. We give a method of obtaining from the combinatorial data of a lightning pair the genus of the resulting Riemann surface.
2.We give a sufficient condition for the completion of the form which is induced from a pre-Tango structure to have non-closed global differential 1-forms. Moreover, we give a lower bound for the dimension of the locus of the curves which have pre-Tango structures inducing such completions, in the moduli space of curves.
3.A Haefliger (6,3)-knot means a smoothly embedded 3-sphere in the 6-sphere. We give a definition of unknotting numbers of Haefliger (6,3)-knots geometrically, and determine the unknotting number of each Haefliger (6,3)-knot.
4.Twisting the Killing vector fields of certain kind of Kerr-Ads black holes, we reproduce the compact Sasaki-Einstein manifolds constructed by Gauntlett, Martelli, Sparks and Waldram. We also discuss an implication of the twist in string theory and M-theory.
5.We construct explicitly a new infinite series of Einstein metrics on the S^3-bundles over S^2, which containing infinite numbers of inhomogeneous ones.
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Research Products
(10 results)
