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2014 Fiscal Year Final Research Report

Differential geometric research on surfaces admitting singularities and its application

Research Project

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Project/Area Number 22540100
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionTokyo Denki University

Principal Investigator

KOKUBU Masatoshi  東京電機大学, 工学部, 教授 (50287439)

Co-Investigator(Renkei-kenkyūsha) UMEHARA Masaaki  東京工業大学, 大学院情報理工学研究科, 教授 (90193945)
YAMADA Kotaro  東京工業大学, 大学院理工学研究科, 教授 (10221657)
ROSSMAN Wayne  神戸大学, 大学院理学研究科, 教授 (50284485)
FUJIMORI Shoichi  岡山大学, 大学院自然科学研究科, 准教授 (00452706)
YAMAMOTO Ou  東京電機大学, 工学部, 教授 (20291700)
IRIE Hiroshi  東京電機大学, 未来科学部, 准教授 (30385489)
Project Period (FY) 2010-04-01 – 2015-03-31
Keywords微分幾何 / 平均曲率 / ガウス曲率 / 特異点
Outline of Final Research Achievements

We studied surfaces admitting singularities in some kind of three-dimensional manifolds of constant curvature, requiring them to have good properties from the differential-geometric viewpoint. (Note that non-Euclidean space of constant curvature have interesting features beyond our common sense.) Concerning linear Weingarten surfaces in hyperbolic space, we had a global representation formula, criterion for the shape of singularities, and a result on the orientability and the co-orientability. Concerning CMC-1 faces in de Sitter space and maxfaces in Lorentz-Minkowski space, we had results on the orientability and the co-orientability. At the same time, the classification of CMC-1 faces having two ends were obtained, and the classification of maxfaces having three ends were obtained.

Free Research Field

微分幾何学とくに曲面論

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Published: 2016-06-03  

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