Invariants On the Geometric Manifolds with Group Actions

具有群作用的几何流形上的不变量

基本信息

批准号：
14340026
负责人：
KAMISHIMA Yoshinobu
金额：
$ 3.97万
依托单位：
Tokyo Metropolitan University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2004
项目状态：
已结题

项目摘要

We have studied a geometric structure on a (4n+3)-dimensional smooth manifold M which is an integrable, nondegenerate codimension 3 subbundle D on M whose fiber supports the structure of 4n-dimensional quaternionic vector space. We call it a psesuo-conformal quterninonic structure. This structure has a refinement which is said to be a psesuo-conformal quterninonic CR structure. The structure is thought of as a generalization of the quaternionic CR structure. In order to study this geometric structure on M, we single out an sp(1)-valued 1-form ω locally on a neighborhood U of M such that Ker ω = D|U. We shall construct the invariants on the pair (M, ω) whose vanishing implies that M is uniformized with respect to a finite dimensional flat quaternionic CR geometry. In fact we have proved the standard psesuo-conformal quterninonic structure on the spahere S^<4n+3> coincides with the standard pseudo-quaternionic CR structure on S^<4n+3> The invariants obtained on a (4n+3)-manifold M have the same formula as the curvature tensor of quaternionic (indefinite) Kaehler manifolds. From this viewpoint, we shall exhibit a quaternionic analogue of Chern-Moser's CR structure. As to the global existence of the 1-form ω on a (4n+3)-manifold M is related to the Pontrjagin classes. We have shown the relation that 2p_1(M)=(n+2)p_1(L). In particular, if 2p_1(M)=0, then there exists a global 1-form co on M which represents a pseudo-conformal quaternionic structure D. As a consequence, there exists a hyperoomplex structure {I, J, K} on D.

我们已经在A（4N+3） - 维平滑歧管M上研究了几何结构，该平滑歧管M是M上可集成的，非数字的编纂3子柱D，其纤维支持4N维Quaternionic载体矢量空间的结构。我们称其为正态的季节性结构。这种结构的改进据说是正态的Quaternionic CR结构。该结构被认为是Quaternionic CR结构的概括。为了在M上研究这种几何结构，我们在M的M邻域u上局部挑出一个SP（1）值1形式的ω，以使KerΩ= D | U。我们将在对（M，ω）上构建不变性，其消失意味着M相对于有限的尺寸平坦的四离子CR几何形状均匀。实际上，我们在Spahere S^<4n+3>上提供了标准的quesu-form-form-farnionic quaternion结构，与S^<4n+3>在S^<4n+3>上的标准伪quaternionic cr结构相吻合（在A（4n+3）-manifold m上获得的不变性，与曲率均具有相同的频率（unde）kae kae kae kae（unde）。从这个角度来看，我们将执行Chern-Moser CR结构的四个离子类似物。至于A（4n+3）-manifold M上1形式ω的全局存在与Pontrjagin类有关。我们已经证明了2p_1（m）=（n+2）p_1（l）的关系。特别是，如果2p_1（m）= 0，则在M上存在一个全局的1形式CO，该CO代表伪符合符合符号的Quaternionic结构D。

项目成果

期刊论文数量（38）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

CR manifolds and transformation groups

CR 流形和变换群

DOI：
发表时间：
2003
期刊：
Selected Topics in CR Geometry (Ed. by S.Dragomir), Quaderni di Matematica. 1329
影响因子：
0
作者：
A.Amarzaya;M.Guest;M.Guest;T.Tsuboi;Toshitake Kohno;Takashi Tsuboi;河野俊丈;河野俊丈;Yoshinobu Kamishima;Yoshinobu Kamishima;Kouji Fujiwara(共著);Yoshinobu Kamishima (L.Ornea);Kouji Fujiwara;神島芳宣;藤原耕二;神島芳宣;神島芳宣
通讯作者：
神島芳宣

Note on realization of cusp cross-sections of complex hyperbolic orbifolds

关于复杂双曲轨道折叠尖点横截面实现的注意事项

DOI：
发表时间：
2003
期刊：
数理研講究録(S.Kamiya (ed.)), Perspectives of Hyperbolic Spaces II 数理解析研究所 1387
影响因子：
0
作者：
A.Amarzaya;M.Guest;M.Guest;T.Tsuboi;Toshitake Kohno;Takashi Tsuboi;河野俊丈;河野俊丈;Yoshinobu Kamishima;Yoshinobu Kamishima;Kouji Fujiwara(共著);Yoshinobu Kamishima (L.Ornea);Kouji Fujiwara;神島芳宣;藤原耕二;神島芳宣
通讯作者：
神島芳宣

神島芳宣: "Three-dimensional Lie group actions on compact (4n+3)-dimensional geometric manifolds"D.flerential geometry and application. 1-26 (2004)

Yoshinobu Kamishima：“紧致 (4n+3) 维几何流形上的三维李群作用”D.flerential 几何和应用。 1-26 (2004)。