Many-sided Research of Foliations

这项研究的目的是从多个角度研究叶序。首席研究员NISHIMORI Toshiyuki(NISHIMORI Toshiyuki)一直在研究相似伪群的定性理论，以发展高余维叶序的定性理论。主要目的是在余维一叶系定性理论中找到经典定理的高次余维类比，并证明了在每个Sacksteder系统中具有气泡的每个轨道的闭包中都存在一个压缩不动点。在这项研究中，首席研究员的目的是找出有气泡的轨道出现的条件。证明了对于每个强半正则轨道，它有气泡当且仅当它有一个有界乘法函数。作为这一结果的某种推广形式，证明了对于每个强半真轨道，几乎有气泡当且仅当它有一个有界的几乎可乘函数。证明的要点是每个强半真轨道都有一个非空的开域。调查者Suwa Tatsuo研究了奇异全纯叶的剩余，得到了一些结果。研究人员以洛伦兹度量为主题的流形上的完全测地线叶理为主题。他们研究了类时叶、类空间叶和类光叶的基本实例和一些结果。

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.