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Riemanian歧管时，不必说，大地测量机构是一个小家族。 。比较定理的命令，以研究由轨迹和轨迹轨道形成的统治的真实表面上的varia型形态安全性新月形的Kaehler歧管。形式。在复杂空间中，地理球上的sasaki磁场考虑奇数减小的磁场。 Kaehler磁场的轨迹不同。 2，包括Kaehler磁场的轨迹家族。订单2 s的外部形状

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

Magnetic mean operators on a Kaehler manifold

Kaehler 流形上的磁平均算子

• 发表时间: 2005
• 期刊: Topics in Almost Hermitian geometry and related fields
• 作者: Akira Kono;Dai Tamaki;Toshiaki ADACHI;Toshiaki ADACHI;Toshiaki ADACHI;Toshiaki ADACHI
• 通讯作者: Toshiaki ADACHI