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Geometries related to foliations

与叶状结构相关的几何形状

基本信息

批准号：
13640055
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：
2001
资助国家：
日本
起止时间：
2001 至 2003
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640055/
关键词：
foliation quaolitative theory similarity pseudogioup exceptional minimal sec

项目摘要

The purpose of tins tesearch was to study foliations from many sided points of view The head investigator (NISHIMORI Toshiyuki) aimed mainly to take several classical theorems in the qualitative theory of codimension one foliations as models and to research about the possibility of making an anaology for foliations of higher codimensions with transverse geometric structures. To say concretely, he considered about the qualitative theory of similarity pseudogroups. As by-products, he expected to obtain new observation about what kind of differences between the codimension one case and the higher codimension case would appear. He paid attention also to the relations between projective anosow flows and bi-contact structures and to totally geodesic foliations of manifolds with Lorentzian metrics as areas with some extent of posibihties.In the period of this study, the head investigator intensively attacked the problem "In what conditons does a strongly semi-proper orbit in a similarity pseudogroup become almost with bubbles?" (He has already proved that analogies of classical theorems in higher codimension cases for orbits almost with bubbles.) The basic idea was that we can divide the total space into territories for points in a strongly semiproper orbit and that the territories become non-empty open subset. He got several conditions under which the territories becomes bubbles for a strongly semi-proper orbits.

本研究的目的是从多个方面研究叶理。主要研究者（西森俊之）的目的主要是以余维1叶理定性理论中的几个经典定理为模型，研究对具有横向几何结构的更高余维叶理进行类比的可能性。具体地说，他考虑了关于相似伪群的定性理论。作为副产品，他希望获得关于余维1情况和更高余维情况之间会出现什么样的差异的新观察。他还注意到之间的关系，投射anosow流和双接触结构和全测地的foliations的流形与洛伦兹度量的领域与某种程度的possibihties。在这一研究期间，首席研究员集中攻击的问题"在什么条件下，一个强半正常轨道在一个相似的伪群成为几乎与泡沫？"（他已经证明了在几乎有气泡的轨道的更高余维情况下经典定理的类比。）其基本思想是，我们可以将整个空间划分为强半真轨道上的点的区域，并且这些区域成为非空的开子集。他得到了几个条件下的领土成为泡沫的一个强半正常轨道。