2004 Fiscal Year Final Research Report Summary
STUDY ON CONDITIONS FOR A SUBGROUP OF PU(1,n ; C) ACTING ON COMPLEX HYPERBOLIC SPACE TO BE DISCRETE
| Project/Area Number |
15540192
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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, PROFESSOR, 工学部, 教授 (80122381)
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| Co-Investigator(Kenkyū-buntansha) |
SHIMENO Nobukazu OKAYAMA UNIVERSITY OF SCIENCE, ASSISTANT PROFESSOR, 理学部, 助教授 (60254140)
TAKENAKA Shigeo OKAYAMA UNIVERSITY OF SCIENCE, PROFESSOR, 理学部, 教授 (80022680)
MURAKAMI Satoru OKAYAMA UNIVERSITY OF SCIENCE, PROFESSOR, 理学部, 教授 (40123963)
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| Project Period (FY) |
2003 – 2004
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| Keywords | COMPLEX HYPERBOLIC SPACE / UNITARY GROUP PU(1,n;C) / DISCRETE GROUP / HEISENBERG TRANSLATION / FUNDAMENTAL DOMAIN / ISOMETRIC SPHERE / JORGENSEN'S INEQUALITY / SHIMIZU'S LEMMA |
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| Research Abstract |
1)We have complex version of Jorgensen's inequality for a subgroups of PU(1,2;C) with boundary elliptic or loxodromic elements to be discrete. We extend stable basin theorems of Kamiya, Basmajian-Miner, which use to generalize Basmajian-Miner's results. We also obtain complex version of Shinizu's lemma for a subgrou of PU(1,2;C) with screw parabolic elements, which is used to construct a precisely invariant region.
2)We define the generalized isometric of an element of PU(1,n;C). By using the generalized isometric spheres of elements of a discrete subgroup of PU(1,n;C), we construct a fundamental domain, which is regarded as a generalization of the Ford domain. And we show the connection between this generalized Ford domain and Dirichlet polyhedron.
3)Now we are ready to study the deformation space.
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