2005 Fiscal Year Final Research Report Summary
Generalizations of Weierstrass-type representation formulae and applications
| Project/Area Number |
14340024
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Kyushu University |
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Principal Investigator |
YAMADA Kotaro Kyushu University, Faculty of Mathematics, Professor, 大学院・数理学研究院, 教授 (10221657)
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| Co-Investigator(Kenkyū-buntansha) |
MIYAOKA Reiko Kyushu University, Faculty of Mathematics, Professor, 大学院・数理学研究院, 教授 (70108182)
SAEKI Osamu Kyushu University, Faculty of Mathematics, Professor, 大学院・数理学研究院, 教授 (30201510)
UMEHARA Masaaki Osaka University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (90193945)
KUROSE Takashi Fukuoka University, Faculty of Science, Associate Professor, 理学部, 助教授 (30215107)
TAKAHASHI Masaro Kurume National College of Technology, Associate Professor, 助教授 (70311107)
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| Project Period (FY) |
2002 – 2005
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| Keywords | Weierstrass representation / singularities / front / maximal surface / flat surface / cuspidal edge / cuspidal cross cap / swallowtail |
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| Research Abstract |
1.W rewrote the Weierstrass-type representation formula for flat surfaces in hyperbolic 3-space in the form without integration (Darboux-type formula), and classified complete flat surfaces with small numbers of ends. 2.We pointed out the class of ambient spaces for which an analogue of Weierstrass-type (Bryant) representation formula for mean curvature one surfaces in hyperbolic 3-space holds. 3.We found criteria for singularities (cuspidal edges, swallowtails, cuspidal cross caps) which are generic singularities of fronts or frontals. 4.We established fundamental notions of flat fronts in hyperbolic 3-space, and investiagted properties of singularities of such surfaces. 5.We defined a certain class of maximal surfaces with singularities in Minkowski 3-space (called maxface), and investigated their singularities.
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