Research of submanifolds in a symmetric space by using infinite dimensional geometry

利用无限维几何研究对称空间中的子流形

基本信息

批准号：
18540099
负责人：
KOIKE Naoyuki
金额：
$ 1.52万
依托单位：
Tokyo University of Science
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2006
资助国家：
日本
起止时间：
2006 至 2007
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18540099/
关键词：
Differential Geoimetry 微分幾可学

项目摘要

As the first study result of 2006, we obtained a Chevalley type restriction theorem for a proper complex equifocal submanifold in a symmetric space of non-compact type. The proof was performed by investigating the lift of its complexification to some infinite dimensional anti-Kaehlerian space. Here we note that principal orbits of Hermann type actions on the symmetric Name are proper complex equifocal submanifolds. This research was performed by the head investigator. As the second study result, we almost classified complex hyperpolar actions with total geodesic orbit on a symmetric space of non-compact type. Here we note that principal orbits of complex hyperpolar actions are complex equifocal submanifolds and that conversely homogeneous complex equifocal submanifolds war as principal orbits of complex hyperpolar actions. Also, we note that Hermann type actions are complex hyperpolar actions. This research was performed by the head investigator. As the third study result, we classified cohomogeneity one actions on rankone symmetric spaces of non-compact type. This research was performed by Professor Hiroshi Tamaru of the investigator and Professor Jurgen Berndt.As the first study result of 2007, we completed almost the proof of the homogeneity theorem for irreducible proper complex equifocal submanifolds of codimension greater than one in a symmetric space of non-compact type. The proof was performed by investigating the lift of its complexification to some infinite dimensional anti-Kaehlerian space. This research was performed by the head investigator. As the second study result, we completed almost the proof of the non-existence theorem of equifocal submanifolds with non-Bat section in an irreducible symmetric space of rank greater than one, which is an open problem. This research was performed by the head investigator.

作为2006年的第一个研究结果，我们获得了雪佛兰类型限制定理，用于在非紧凑型类型的对称空间中适当的复杂地球次序列。该证明是通过研究将其络合力提升到某些无限尺寸的反kaehlerian空间来进行的。在这里，我们注意到，对称名称上Hermann类型动作的主要轨道是适当的复杂的Equifocal Submanifolds。这项研究是由首席调查员进行的。作为第二项研究结果，我们几乎将与总测量轨道的总测量轨道分类为非紧凑类型的对称空间。在这里，我们注意到，复杂的超极作用的主要轨道是复杂的地球次序，相反，相反的复杂的复杂的equifocal equifocal Submanifolds战争是复杂的超极作用的主要轨道。另外，我们注意到Hermann型动作是复杂的超极作用。这项研究是由首席调查员进行的。作为第三个研究结果，我们将同一均匀性分类为一项对非紧凑类型的Rankone对称空间的作用。这项研究是由研究人员和尤尔根·伯恩特（Jurgen Berndt）教授塔玛鲁（Hiroshi Tamaru）教授进行的。作为2007年的第一个研究结果，我们几乎完成了在非典型类型的对称空间中，几乎可以证明，不可还原适当的适当复杂的地位象征的均质定理的证明。该证明是通过研究将其络合力提升到某些无限尺寸的反kaehlerian空间来进行的。这项研究是由首席调查员进行的。作为第二项研究结果，我们几乎完成了与非蝙蝠截面的不存在的不存在的定理的证明，在不可减少的对称级别大于一个大于一个，这是一个空旷的问题。这项研究是由首席调查员进行的。