Many-sided Research of Foliations

叶状结构的多方面研究

• 批准号: 10640053
• 负责人: NISHIMORI Toshiyuki
• 金额: $ 1.92万
• 依托单位: HOKKAIDO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640053/
• 关键词: qualitative theory; foliation; similarity pseudogroup; Sacksteder's Theorem; exceptional minimal set; 葉層構造; 留数理論; ミルナー数; 非ユニモデュラーリー群; 指数公式; ウエッブ; ブラシュケ接続; 区分線形同相群

The purpose of this research was to study foliations from many sided points of view.The head investigator (NISHIMORI Toshiyuki) had been studying the qualitative theory of similarity pseudogroup in order to develop the qualitative theory of foliations of higher codimension. The main theme was to find a higher codimensional analogy of classical theorems in the qualitative theory of codimension-one foliations, and proved that there is a fixed point of a contraction in the closure of each orbits with bubbles in each Sacksteder system. In this research, the aim of the head investigator was to find the condition under which orbits with bubbles appear. As a results, it was proved that, for each strongly semiproper orbit, it is with bubbles if and only if it has a bounded multiplicative function. As a somewhat generalized version of this result, it was proved that, for each strongly semiproper orbit, it is almost with bubbles if and only if it has a bounded almost multiplicative function. The point of the proof was each strongly semiproper orbit has a non-empty open territory.The investigator SUWA tatsuo studied the residues of singular holomorphic foliations and obtained some results. The investigators took totally geodesic foliations on manifolds with Lorentzian metric as the theme. They studied fundamental examples of timelike leaves, spacelike leaves and lightlike leaves and some results.

本研究的目的是从多个角度研究叶理。首席研究员（西森俊之）一直在研究相似伪群的定性理论，以发展更高余维的叶理的定性理论。主要的主题是找到一个更高的余维类比的经典定理的定性理论的余维一叶理，并证明有一个不动点的收缩封闭的每个轨道的泡沫在每个Sacksteder系统。在这项研究中，首席研究员的目的是找到气泡轨道出现的条件。结果证明了，对于每个强半真轨道，它是有泡的当且仅当它有一个有界乘法函数。作为这个结果的某种推广，证明了对于每个强半真轨道，它几乎有泡当且仅当它有一个有界的几乎乘法函数。证明的要点是每个强半真轨道都有一个非空的开域。研究者SUWA Tatsuo研究了奇异全纯叶理的剩余，得到了一些结果。研究者们以洛伦兹度量为主题，研究流形上的全测地叶理。他们研究了类时叶、类空叶和类光叶的基本例子和一些结果。

项目成果

Suwa, Tatsuo: "Generalization of variations and Baum-Bott residues for holomorphic foliations on singular varieties"Intern. J. of Math.. 10. 367-384 (1999)

Suwa, Tatsuo：“奇异品种全纯叶状结构的变异和 Baum-Bott 残基的概括”实习生。

Suwa,Jatsuo: "Dual class of a suovariety"Tokyo J.Math.. 23. 51-68 (2000)

诹访Jatsuo：“多品种的双类”Tokyo J.Math.. 23. 51-68 (2000)

Brasselet, J.-P.: "Nash residues of singular holomorphic foliations"Asian J.Math.. 14. 37-50 (2000)

Brasselet, J.-P.：“奇异全纯叶的纳什残基”亚洲 J.Math.. 14. 37-50 (2000)

Suwa, Tatsuo: "Dual class of a subvariety"Tokyo J.Math.. 23. 51-68 (2000)

诹访辰夫：“亚品种的双类”Tokyo J.Math.. 23. 51-68 (2000)

Suwa, Tatsuo: "Milnor numbers and classes of local complete intersections"Proc. Japan Acad.. 75. 179-183 (1999)

Suwa，Tatsuo：“局部完整交叉路口的米尔诺数量和类别”Proc。