权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

多様体の幾何構造変形の可視化

流形几何结构变形可视化

基本信息

批准号：
08640092
负责人：
小島定吉
金额：
$ 1.41万
依托单位：
Tokyo Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至无数据
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08640092/
关键词：
多様体双曲多様体幾何構造 Dehn手術可視化

项目摘要

多様化の幾何構造の研究には,様々な数学の側面が現れる.本研究では,研究組織のメンバーの多岐にわたる専門領域と,メンバーが在籍する数理・計算科学専攻の計算機環境を拠り所に,他機関の研究者も含め相互研究交流を日常的にとりながら,幾何構造の変形の研究を進めた.具体的な変形操作として,「3次元双曲多様体の双曲デーン手術」と「サークルパッキングを用いた閉曲面の射影構造の変形」を取り上げた.前者については,コンピュータ上での仮想計算をよりどころに,錐状の特異集合を許容する3次元双曲錐多様体の大域変形の可能性について,いろいろ理論的な結果を得た.たとえば双曲結び目の分岐被覆には,1つの例外を除いて,分岐指数が3以上であれば常に双曲構造が入ることをなど.現在成果をまとまた論文を投稿中である.後者については,当初計画していた種数2以上の閉曲面の射影構造の変形論は計算に多大な困難を伴うことが分かったため,種数を1にし,サークルパッキングを使ったトーラスの複素アフィン構造の変形に対象を変えた.そして変形に従うパッキングの変化を,展開写像を通して平面上に可視化した.またこうした実験数学的なアプローチをもとに,変形が予想どおり局所的に実2次元分あることを示した.これらの実験数学的取組みや理論的考察には,分担者および海外を含む1他の機関の研究者との間の交流により得られた様々なアイデアをフルに使った.研究の性格上多くの専門家との交流が不可欠であったため,研究連絡および専門的知識の提供依頼が頻繁にあり,研究費のかなりの部分を旅費および謝金にあてた.

In many ways, there is no way to make a research, and there is a problem in mathematics. In this study, research organizations are involved in the field of research, mathematical and physical computing, computer science, and the environment. Other researchers are involved in the daily research and exchange of mutual research and communication, and how to improve the research on the shape of computers. The specific shape operation is accurate, "three-dimensional hyperbolic multi-body, hyperbolic, hyperbolic and hyperbolic. In the former, we want to calculate the possibility of the shape of the three-dimensional hyperbolic multi-body, and the results of the theory of the theory are obtained. Hyperbolic results show that bifurcation is covered, except that bifurcation index is more than 3, bifurcation index is more than 3. Now I am in the process of submitting the results and articles. In the latter part, it was planned that the number of figures was more than 2, the surface was projected, the shape was built, the shape was calculated, the size of the computer was calculated, and the number of images was calculated. In this way, you can change the shape of the image, spread it out and write it on the plane like the one that can be changed. I don't know. I don't know. Based on the review of the theory of mathematical composition and theory, the distributor is involved in the study of the theory of mathematics, and the distributor is interested in the theory of mathematics. In the study of personality, there are many people in the family to communicate with each other, and the knowledge of people who are linked to each other should be provided in accordance with their knowledge, and the research should be based on the number of people who travel.