Ruled real surfaces formed by Kaehler magnetic fields

由凯勒磁场形成的直纹真实表面

• 批准号: 17540072
• 负责人: ADACHI Toshiaki
• 金额: $ 2.32万
• 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: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17540072/
• 关键词: Kaehler magnetic field; trajectory; geodesic sphere; structure torsion; length spectrum; extrinsic shape of a curve; curvature lovarithmic derivative; Hermitian symmetric space; extrinsic shape; isoymetric immersion; umbilic point; isotropic

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

当我们研究Riemannian歧管时，有必要说大地测量公司起着非常重要的对象。但是，如果我们考虑所有平滑曲线的家族，那么大师家族就是一个小家庭。由于这个原因，调查员通过研究Kaehler磁场的轨迹来研究Kaehler流形，这是Kaehler form1.com的持续倍数。在对Kaehler歧管的截面曲率的假设下，我们可以按照复杂空间形式的相应物体的长度来估算这些物体的电路长度。2。在复杂空间形式的Sasaki磁场上的sasaki磁场的trajextories我们考虑奇数尺寸歧管上的Sasaki磁场。这对应于实际EAVN维歧管上的Kaehler磁场。尽管COM中的大地球形面积……更多的PLEX空间形式是模型空间，但Sasaki磁场的轨迹的性质与复杂空间形式的Kaehler磁场的轨迹属性完全不同。有些轨迹具有相同的长度，但并非彼此一致。3。通过等距浸入式的某些kaehler歧管的特征，通过等距沉浸式浸入真实空间形式。由于等距浸入对流形的结构刚度有一定的结构刚度，因此我们认为曲线的家族具有阶点2，其中包括Kaehler磁场的轨迹家族。我们可以将完全脐带浸入或第一标准嵌入的复杂空间形式表征为诱导地图保存命令2属性和曲率对数衍生物的复杂空间形式。如果我们将订单2属性的条件削弱到其外部形状为2的条件，那么我们可以表征居民对称空间的等级少于3

项目成果

Schur's lemma for K\"ahler manifolds

K"ahler 流形的 Schur 引理

• 发表时间: 2008
• 期刊: Arch. Math 90
• 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

• 发表时间: 2005
• 期刊: Topology and its application 146-147
• 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

• 发表时间: 2005
• 期刊: Topology and its application 146-147
• 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

• 发表时间: 2007
• 期刊: Hokkaido Math. J. 36
• 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

• 发表时间: 2006
• 期刊: Monatshefte fur Mathematik 149
• 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