Ruled real surfaces formed by Kaehler magnetic fields
由凯勒磁场形成的直纹真实表面
基本信息
- 批准号:17540072
- 负责人:
- 金额:$ 2.32万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (C)
- 财政年份:2005
- 资助国家:日本
- 起止时间:2005 至 2007
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
When we study Riemannian manifolds, it is needless to say that geodesics play quite important object. But if we consider the family of all smooth curves, the family of geodesics is a small family. In this reason the head investigator studied Kaehler manifolds by investigating trajectories for Kaehler magnetic fields, which are constant multiples of the Kaehler form1.Comparison theoremsIn order to study Kaehler manifolds of variable holomorphic sectional curvatures, we consider crescents on a ruled real surface formed by trajectory and trajectory-sectors. Under an assumption on sectional curvatures of a Kaehler manifold, we can estimate lengths of circuits of these objects by length of corresponding objects on a complex space form.2.Trajectories for Sasaki magnetic fields on geodesic spheres in a complex space formWe consider Sasaki magnetic fields on odd dimensional manifolds. This corresponds to Kaehler magnetic fields on real eavn dimensional manifolds. Though geodesic spheres in com … More plex space forms are model spaces, properties of trajectories for Sasaki magnetic fields are quite different from properties of trajectories for Kaehler magnetic fields on complex space forms. There are trajectories which have the same length but are not congruent to each other.3.Characterizations of some Kaehler manifolds through isometric immersionsWe study Kaehler manifolds through isometric immersions into real space forms. Since isometric immersions give some structural rigidity on manifolds, we consider the family of curves having points of order 2, which includes the family of trajectories for Kaehler magnetic fields. We can characterize complex space forms immersed by totally umbilic immersions or 1st standard embeddings as those whose induced maps preserve order 2 property and curvature logarithmic derivative. If we weaken the condition on order 2 property to the condition that their extrinsic shapes are of order 2, then we can characterize Hermitian symmetric spaces of rank less than 3 Less
在研究黎曼流形时,测地线无疑是一个重要的研究对象。但是如果我们考虑所有光滑曲线的族,测地线族是一个小族。因此,首席研究员通过研究卡勒磁场的轨迹来研究卡勒流形,卡勒磁场是卡勒形式的常数倍。比较定理为了研究可变全纯截面曲率的Kaehler流形,我们考虑由轨迹和轨迹扇区构成的直纹实曲面上的新月。在对Kaehler流形截面曲率的假设下,我们可以用复空间形式2上对应对象的长度来估计这些对象的回路长度。复杂空间形式下测地线球上佐佐木磁场的轨迹我们考虑奇维流形上的佐佐木磁场。这对应于实际四维流形上的凯勒磁场。更复杂的空间形式是模型空间,但Sasaki磁场的轨迹性质与Kaehler磁场在复杂空间形式上的轨迹性质有很大不同。有些轨迹长度相同,但彼此不相等。一些Kaehler流形的等长浸没表征我们通过等长浸没到真实空间形式来研究Kaehler流形。由于等距浸入在流形上具有一定的结构刚性,我们考虑具有2阶点的曲线族,其中包括Kaehler磁场的轨迹族。我们可以将完全脐带浸没或第一标准浸没的复杂空间形式描述为其诱导映射保持2阶性质和曲率对数导数的空间形式。如果我们将2阶性质的条件弱化为其外在形状为2阶的条件,那么我们就可以刻画秩小于3的厄米对称空间
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Schur's lemma for K\"ahler manifolds
K"ahler 流形的 Schur 引理
- DOI:
- 发表时间:2008
- 期刊:
- 影响因子:0
- 作者:T. Adachi;S. Maeda;S. Udagawa
- 通讯作者:S. Udagawa
Kaehler magnetic flows for a product of complex space forms
复杂空间形式产物的凯勒磁流
- DOI:
- 发表时间:2005
- 期刊:
- 影响因子:0
- 作者:Toshiaki;ADACHI;Dai Tamaki;Toshiaki ADACHI;Toshiaki ADACHI;Dai Tamaki;Toshiaki ADACHI;Dai Tamaki;Dai Tamaki;Sadahiro MAEDA;Dai Tamaki;Sadahiro MAEDA;Dai Tamaki;Sadahiro MAEDA;Dai Tamaki;Toshiaki ADACHI
- 通讯作者:Toshiaki ADACHI
Holomorphic helix of proper order 3 on a complex hyperbolic plane
复双曲平面上的真阶 3 全纯螺旋
- DOI:
- 发表时间:2005
- 期刊:
- 影响因子:0
- 作者:河野明;玉木大;Toshiaki ADACHI
- 通讯作者:Toshiaki ADACHI
Geodesic spheres in a nonflat complex space form and their integral curves of characteristic vector fields
非平坦复空间形式的测地球及其特征向量场积分曲线
- DOI:
- 发表时间:2007
- 期刊:
- 影响因子:0
- 作者:T. Adachi;Y.H. Kim;S. Maeda
- 通讯作者:S. Maeda
Practical criterion for some submanifolds to be totally geodesic
一些子流形完全测地线的实用标准
- DOI:
- 发表时间:2006
- 期刊:
- 影响因子:0
- 作者:Toshiaki;ADACHI;Dai Tamaki;Toshiaki ADACHI;Toshiaki ADACHI;Dai Tamaki;Toshiaki ADACHI;Dai Tamaki;Dai Tamaki;Sadahiro MAEDA;Dai Tamaki;Sadahiro MAEDA
- 通讯作者:Sadahiro MAEDA
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ADACHI Toshiaki其他文献
Asymptotic behaviors of trajectories on a Hadamard Kaehler manifold
Hadamard Kaehler 流形上轨迹的渐近行为
- DOI:
10.3836/tjm/1502179311 - 发表时间:
2020 - 期刊:
- 影响因子:0.6
- 作者:
SHI Qingsong;ADACHI Toshiaki - 通讯作者:
ADACHI Toshiaki
ADACHI Toshiaki的其他文献
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{{ truncateString('ADACHI Toshiaki', 18)}}的其他基金
Ideal boundary of a Hadamard manifold and Kaehler magnetic fields
阿达玛流形和凯勒磁场的理想边界
- 批准号:
24540075 - 财政年份:2012
- 资助金额:
$ 2.32万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Kaeler magnetic fields and graphs
凯勒磁场和图表
- 批准号:
20540071 - 财政年份:2008
- 资助金额:
$ 2.32万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Comparison on bow-shapes for Kaehler magnetic fields
凯勒磁场弓形比较
- 批准号:
14540075 - 财政年份:2002
- 资助金额:
$ 2.32万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Kaeler magnetic fields and Carnot spaces
凯勒磁场和卡诺空间
- 批准号:
11640073 - 财政年份:1999
- 资助金额:
$ 2.32万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
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