Geometries related to foliations

TINS研究的目的是从多个角度研究叶理，首席研究员NISHIMORI Toshiyuki的主要目的是以余维一叶理定性理论中的几个经典定理为模型，研究具有横向几何结构的高余维叶理的类型学的可能性。具体地说，他考虑了相似伪群的定性理论。作为副产品，他希望获得新的观察结果，即协维度1的情况与协维度更高的情况之间会出现什么样的差异。他还注意了射影Anosow流与双接触结构之间的关系，以及具有洛伦兹度量的流形上的全测地叶作为具有一定程度正性的区域。在本研究期间，首席研究员集中讨论了这样一个问题：在什么条件下相似伪群中的强半真轨道几乎变得有气泡？(他已经证明，在高余维情况下，经典定理的类比几乎是有气泡的轨道。)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领地，并且领地成为非空的开子集。他得到了几个条件，在这些条件下，区域变成了强半真轨道的泡泡。

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.