2009 Fiscal Year Final Research Report
Study on discrete subgroups of PU(1,2;C) acting on complex hyperbolic 2-space
| Project/Area Number |
19540204
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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 |
Basic analysis
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| Research Institution | Okayama University of Science |
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Principal Investigator |
KAMIYA Shigeyasu Okayama University of Science, 工学部, 教授 (80122381)
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| Co-Investigator(Kenkyū-buntansha) |
YAMASAKI Masayuki 岡山理科大学, 理学部, 教授 (70174646)
TAKENAKA Shigeo 岡山理科大学, 理学部, 教授 (80022680)
MURAKAMI Satoru 岡山理科大学, 理学部, 教授 (40123963)
SHIMENO Nobukazu 岡山理科大学, 理学部, 准教授 (60254140)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 離散群 / 複素双曲空間 |
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| Research Abstract |
We have studied discrete subgroups of PU(1,2;C) acting on complex hyperbolic 2-space.
(1) It is important to find out some conditions for a group to be discrete. For a subgroup of PU(1,2;C) containing a parabolic element, we obtain a complex hyperbolic version of Shimizu's lemma. Using this, we can construct a precisely invariant region, which is useful for construction of fundamental domain for a discrete group.
(2) We have studied complex hyperbolic triangle groups and discussed their discreteness. We found several discrete complex hyperbolic triangle groups.
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