1998 Fiscal Year Final Research Report Summary
Study of metric properties of Teichmuller spaces
| Project/Area Number |
09640176
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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 |
解析学
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| Research Institution | Nagoya University |
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Principal Investigator |
NAKANISHI Toshihiro Graduate School of Mathematics, Nagoya University Associate Professor, 大学院・多元数理科学研究科, 助教授 (00172354)
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| Co-Investigator(Kenkyū-buntansha) |
YOKOYAMA Misako Faculty of Science Shizuoka University, Assistant, 理学部, 助手 (80240224)
SATO Hiroki Faculty of Science Shizuoka University, Professor, 理学部, 教授 (40022222)
IZEKI Hiroyasu Graduate School of Science Tohoku University, Associate Professor, 大学院・理学研究科, 助教授 (90244409)
TANIGAWA Harumi Graduate School of Mathematics Assistant, 大学院・多元数理科学研究科, 助手 (30236690)
YOSHIKAWA Ken-ichi Graduate School of Mathematics Assistant, 大学院・多元数理科学研究科, 助手 (20242810)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Teichmuller Space / Riemann Surface / Hyperbolic Geometry / Kleinian Groups |
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| Research Abstract |
We have studied metric properties of Teichmuller space of 2 dimensional hyperbolic orbifolds and related subjects on discontinuous groups and 2 and 3 dimensional orbifolds. We obtained the following results :
1. Description of Teichmuller space of hyperbolic cone surfaces as a real algebraic space by using the distances between cone points and horocycles and its applications to the problem of finding the minimal number of geodesic length functions needed for a global parametrization of a Teichmuller space, the representation of mapping class groups and holomorphic families of Riemann surfaces.
2. Geodesic length functions related to suitably chosen closed curves on the underlying surface of a cone surface supply a global coordinate-system on the Teichmuller space. We expressed the 2 form which is defined analogously to Wolpert's formula of Weil-Petersson 2-form in terms of these geodesic length functions and calculated the volumes of some moduli spaces.
3. Classification of all non-cocompact arithmetic. Fuchsian groups of signature (0 ; theta_1, theta_2, theta_3, theta_4).
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