Geometric variational problems and submanifolds.
几何变分问题和子流形。
基本信息
- 批准号:11640057
- 负责人:
- 金额:$ 1.98万
- 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:1999
- 资助国家:日本
- 起止时间:1999 至 2000
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
First we invetigated 3-dimensional minimal submanifolds with 2-parameter family of great spheres in a sphere S^n. Set of (oriened) great circles is identified with real (oriented) 2-plane Grassmannian and the complex quadric Q^<n-1> in a complex projective space. Then the submanifold M with 2-parameter family of great spheres in S^n is constructed as a circle bundle over a 2-dimensional surface Σ in Q^<n-1>. We showed that (1) Σ is a complex 1-dimensional holomorphic curve in Q^<n-1>, then the Gauss mapping of the corresponding submanifold M in S^n is degenerate, (2) the holomorphic curve Σ in Q^<n-1> is first order isotropic, then the corresponding M is minimal.Next, by a joint research with Goo Ishikawa (Hokkaido Univ.) and Reiko Miyaoka (Sophia Univ.), we generalized the former results to higher dimensional submanifolds in spheres. Especially, if a complex submanifold Σ in Q^<n-1> is first order isotropic, then the corresponding submnanifold M (circle bundle over Σ) with (dim_R Σ)-parameter family of great spheres in S^n is austere. Hence we can construct special Lagrangian submanifolds in complex Euclidean spaces by using the results with respect to the calibration by Harvey and Lawson. And we showed that from some homogeneous submanifolds in real Grassmannians of rank 2, 3, 5, one can construct homogeneous austere submanifolds M in S^n such that the Gauss mapping of M is degenerate and satisfying Ferus' equality. They are a natural generalization of E.Cartan's isoparametric hypersurfaces.
首先研究了球面S^n中具有2-参数大球族的三维极小子流形。(有向)大圆集与复射影空间中的真实的(有向)2-平面格拉斯曼和复二次曲面Q^相同<n-1>。然后将S^n中具有2-参数大球面族的子流形M构造为Q^n中二维曲面上的圆丛<n-1>。我们证明了:(1)如果Q^中的全纯曲线是复1维<n-1>的,则相应子流形M在S^n中的Gauss映射是退化的;(2)如果Q^中的全纯曲线<n-1>是一阶迷向的,则相应子流形M是极小的。和Reiko Miyaoka(上智大学),我们把以前的结果推广到球面中的高维子流形。特别地,如果Q^n中的复子流形M<n-1>是一阶迷向的,则S^n中相应的具有(dim_R)-参数族的大球面的子流形M(M上的圆丛)是严格的.利用Harvey和Lawson关于标定的结果,我们可以在复欧氏空间中构造特殊的拉格朗日子流形。证明了从秩为2,3,5的真实的Grassmannian中的某些齐次子流形中,可以构造S^n中的齐次严格子流形M,使得M的Gauss映射退化并满足Ferus等式.它们是E.Cartan等参超曲面的自然推广。
项目成果
期刊论文数量(22)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
T.Adachi,M.Kimura & S.Mueda: "A characterization of all homogeneous real hyperson faces in a complex projective space by observing the extrinsic shape of seal."Arch.Math.. 73・4. 303-310 (1999)
T.Adachi、M.Kimura 和 S.Mueda:“通过观察密封的外在形状来表征复杂射影空间中的所有同质真实超子面。”Arch.Math.. 73・4(1999)。
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- 影响因子:0
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- 通讯作者:
木村真琴: "Miminal immers as of came aicle bur***"Osaka J. Meth. (予定).
Makoto Kimura:“Miminal immers as of come aicle bur***”Osaka J. Meth(计划中)。
- DOI:
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- 影响因子:0
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Makoto Kimura: "Minimal immersions of some circle bundles over holomorphic curves in complex quadric to sphere"Osaka Math.J.. Vol.37. 883-903 (2000)
Makoto Kimura:“复二次曲面到球面上的一些圆束在全纯曲线上的最小浸没”Osaka Math.J. Vol.37。
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- 影响因子:0
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Makoto Kimura and Sadahiro Maeda: "Geometric meaning of isoparametric hypersurfaces in a real space form"Canad.Math.Bull.. Vol.43. 74-78 (2000)
Makoto Kimura 和 Sadahiro Maeda:“实空间形式中等参超曲面的几何意义”Canad.Math.Bull.. Vol.43。
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- 影响因子:0
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- 通讯作者:
T.Adachi & S.Mueda: "Space forms for the viewpoint of their geodesic sphere"Bull.Austral.Math.Soc.. 62. 205-201 (2000)
足立
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KIMURA Makoto其他文献
A twistor construction of Hopf real hypersurfaces in complex hyperbolic space
复双曲空间中Hopf实超曲面的扭量构造
- DOI:
10.2969/jmsj/88968896 - 发表时间:
2023 - 期刊:
- 影响因子:0.7
- 作者:
CHO Jong Taek;KIMURA Makoto;ORTEGA Miguel - 通讯作者:
ORTEGA Miguel
KIMURA Makoto的其他文献
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{{ truncateString('KIMURA Makoto', 18)}}的其他基金
Mineralogical study on the formation process of chondrites
球粒陨石形成过程的矿物学研究
- 批准号:
22540488 - 财政年份:2010
- 资助金额:
$ 1.98万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Structure-activity relationship and thermostability of ribonucleoprotein enzyme
核糖核蛋白酶的构效关系及热稳定性
- 批准号:
22380062 - 财政年份:2010
- 资助金额:
$ 1.98万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Community Empowerment through participatory unpaved road maintenance in Papua New Guinea
巴布亚新几内亚通过参与式未铺砌道路维护增强社区权能
- 批准号:
21404006 - 财政年份:2009
- 资助金额:
$ 1.98万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Geometry of Lagrange submanifolds and Ricci solitons
拉格朗日子流形和里奇孤子的几何
- 批准号:
21540083 - 财政年份:2009
- 资助金额:
$ 1.98万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Role of bacteriophage communities in paddy soils and their gene diversity and uniqueness
水稻土中噬菌体群落的作用及其基因多样性和独特性
- 批准号:
21380046 - 财政年份:2009
- 资助金额:
$ 1.98万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Evaluation of design method of embankment including arch culverts with harmony of landscape
拱涵路堤景观协调设计方法评价
- 批准号:
21360224 - 财政年份:2009
- 资助金额:
$ 1.98万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Elucidation of genetic mechanisms that generate structural diversity of a group of sesquiterpenes involved in plant-microbe interactions
阐明产生一组参与植物-微生物相互作用的倍半萜烯结构多样性的遗传机制
- 批准号:
20580117 - 财政年份:2008
- 资助金额:
$ 1.98万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
A study on Samguk-yusa
三国游学研究
- 批准号:
20520618 - 财政年份:2008
- 资助金额:
$ 1.98万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Study on the mechanism of the ribonucleoprotein complex
核糖核蛋白复合物的作用机制研究
- 批准号:
19380060 - 财政年份:2007
- 资助金额:
$ 1.98万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Study on formation process and chronology of chondrites
球粒陨石形成过程及年代学研究
- 批准号:
19540500 - 财政年份:2007
- 资助金额:
$ 1.98万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
相似海外基金
Geometry of Gauss Mapping
高斯映射的几何
- 批准号:
13640073 - 财政年份:2001
- 资助金额:
$ 1.98万 - 项目类别:
Grant-in-Aid for Scientific Research (C)