Comparison on bow-shapes for Kaehler magnetic fields

凯勒磁场弓形比较

基本信息

批准号：
14540075
负责人：
ADACHI Toshiaki
金额：
$ 2.24万
依托单位：
Nagoya Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
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

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540075/
关键词：
Kaehler magnetic fields crescent trajectories Jacobi fields magnetic exponential maps sectors comparison theorem magnetic flow trajectory magnetic Jacobi fields complex space form bow shape Kaehler magnetic field variation of geo

项目摘要

The head of investigator mainly studied real 2-dimensional surfaces which are naturally obtained from trajectories for Kaehler magnetic fields. He compared such surfaces on complex space forms with such surfaces on general Kaehler manifolds..(1)Comparison on bow-shapes and crescentsGiven a trajectory for a Kaehler magnetic field, we attach at each point on this trajectory a geodesic whose initial vector and the tangent vector of trajectory span a complex line in the tangent space. Such geodesics form a real 2-dimensional surfece. On a complex space form this surface is a complex space line. In order to study tie shape of this surfece on a general Kaehler manifold, for a part of this trajectory we take a geodesic segment on this surfece which joins its ends. Under the condition of sectional curvature from above, we find the length of the geodesic segment is not shorter than the length of bow-shape on a complex space form. We also find that the equality holds if and only if the crescent … More is totally geodesic immersed bow-shape.(2)Comparison on sectorsWe consider an image of a complex line through magnetic exponential map. On a complex space form the image of r-ball in a tangent complex line is an intersection of geodesic r-ball and a complex space line. In order to study this sector on a general Kaehler manifold, we consider the length of arc of this sector. Under the condition of sectional curvature from below, we find the length of the arc is not longer than the length of arc of a corresponding sector on a complex space form. We also find that the equality holds if and only if the sector is totally geodesic and complex embedded one.(3)Variation of force and pseudo-congruency of Kaehler magnetic flowsThough we have a real 2-dimensional surface which is obtained by varying forces of Kaehler magnetic fields, it is not so natural on a general Kaehler manifold in view of mappings. Using this property we studied pseudo-congruency of Kaehler magnetic flows on a Kaehler manifold with complex Euclidean factor. As an application we characterize the rank of Hermitian symmetric space of noncompact type in terms of force of Kaehler magnetic field with horocycle trajectories. Less

课题组长主要研究了从凯勒磁场轨迹自然获得的真实二维曲面，他将复杂空间形式上的曲面与一般凯勒流形上的曲面进行了比较。(1)弓形和新月形的比较。对于凯勒磁场的轨迹，我们在该轨迹上的每个点上附加一条测地线，其初始向量和轨迹的切向量跨越切线空间中的一条复线，这样的测地线形成了一条实数。在一个复杂的空间形式上，这个表面是一个复杂的空间线，为了研究这个表面在一般凯勒流形上的连接形状，对于这个轨迹的一部分，我们在这个表面上采用一个测地线段来连接它。在上面的截面曲率条件下，我们发现测地线段的长度不小于复杂空间形式上的弓形的长度，我们还发现该等式成立当且仅当新月……完全是测地线浸没弓形。 (2)扇区比较我们通过磁指数图考虑复线的图像，在复空间上，切线复线中的r球的图像是测地线的交点。 r-球和复杂空间线为了在一般凯勒流形上研究该扇形，我们在截面曲率条件下考虑该扇形的弧长，求出该弧长。不长于复空间形式上相应扇形的弧长，当且仅当该扇形是完全测地线且复嵌入的扇形时，该等式成立。(3)力的变化和伪全等。凯勒磁流虽然我们有一个通过改变凯勒磁场的力获得的真实二维表面，但从映射的角度来看，它在一般凯勒流形上并不那么自然，我们使用这个属性研究了伪同余性。具有复欧几里德因子的凯勒流形上的凯勒磁流作为一种应用，我们用具有少环轨道的凯勒磁场力来表征非紧型埃尔米特对称空间的等级。

项目成果

期刊论文数量（43）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Geometry of ordinary helices in a complex projective space

复杂射影空间中普通螺旋的几何形状

DOI：
发表时间：
2004
期刊：
Hokkaido Journal of Mathematics 33
影响因子：
0
作者：
T.Adachi;S.Maeda;S.Udagawa
通讯作者：
S.Udagawa

Characterization of complex space forms in terms of geodesies on their geodesic spheres

根据测地线球上的测地线来表征复杂空间形式

DOI：
发表时间：
2003
期刊：
Nihonkai Journal of Mathematics 14
影响因子：
0
作者：
Toshiaki ADACHI;Toshiaki ADACHI;Toshiaki ADACHI;Toshiaki ADACHI;Toshiaki ADACHI;Toshiaki ADACHI;Toshiaki ADACHI;Toshiaki ADACHI;Sadahiro MAEDA;Sadahiro MAEDA;Toshiaki ADACHI
通讯作者：
Toshiaki ADACHI

Curves and submanifolds in a symmetric space of rank one(in Japanese)

一阶对称空间中的曲线和子流形（日语）