The study of relations between the cone structures associated with foliations and their differential geometric properties.
研究与叶状结构相关的锥体结构及其微分几何特性之间的关系。
基本信息
- 批准号:16540050
- 负责人:
- 金额:$ 2.3万
- 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:2004
- 资助国家:日本
- 起止时间:2004 至 2006
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
1)The notion of admissible functions for digraphs is introduced, and given a correspondence between Riemannian metrics of foliated manifolds and labeling of digraphs associated to the foliation. As an application, we give a divergence-like characterization of admissible functions on digraphs. We also show this fact directly via purely graph theoretical view point.2)It is shown that for any vector filed N transverse to the given foliation, there are many functions f so that fZ be a mean curvature vector field of the foliation with respect to some Riemannian metric. A characterization of such vector fields are given by studying the cone structure associated to the foliation.3)It is shown that the result stated in (2)can be extended to the case when the plane field is not integrable. It is also shown that, as an application of this characterization, mean curvature vector fields and functions have a stable property with respect to the variations of plane fields.4)Studying Waring Problem by using circle method, new method of estimation of the integrals over minor arcs is obtained.
1)引入了有向图的容许函数的概念,给出了有叶流形的黎曼度量与有向图的标号之间的对应关系。作为应用,我们给出了有向图上可容许函数的类散度刻画。我们还用纯图论的观点直接证明了这一事实。2)证明了对于任何横跨给定叶层的向量场N,都有许多函数f使得Fz是该叶层相对于某种黎曼度量的平均曲率向量场。3)证明了(2)中的结果可以推广到平面场不可积的情况。作为这一刻划的应用,平均曲率向量场和平均曲率向量场函数对于平面场的变化具有稳定的性质。4)利用圆法研究Wering问题,得到了估计小圆弧上积分的新方法。
项目成果
期刊论文数量(30)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
On sums of sixteen biquadrates.
十六个二次方之和。
- DOI:
- 发表时间:2005
- 期刊:
- 影响因子:0
- 作者:J.-M. Deshouillers;K. Kawada and T. D. Wooley
- 通讯作者:K. Kawada and T. D. Wooley
Some properties of mean curvature vectors for codimension-one Foliations.
余维一叶状体的平均曲率向量的一些性质。
- DOI:
- 发表时间:2005
- 期刊:
- 影响因子:0
- 作者:Hideya Hashimoto;Takashi Koda;Katsuya Mashimo;Kouei Sekigawa;G.Oshikiri
- 通讯作者:G.Oshikiri
A divergence-like characterization of admissible functions on Digraphs : A combinatorial proof.
有向图上允许函数的类散度表征:组合证明。
- DOI:
- 发表时间:2004
- 期刊:
- 影响因子:0
- 作者:J.-M.Deshouillers;K.Kawada;T.D.Wooley;G.Oshikiri;G.Oshikiri;G.Oshikiri
- 通讯作者:G.Oshikiri
On sums of sixteen biquadrates
十六个二次方之和
- DOI:
- 发表时间:2005
- 期刊:
- 影响因子:0
- 作者:J.-M. Deshouillers;K. Kawada and T. D. Wooley
- 通讯作者:K. Kawada and T. D. Wooley
A divergence-like characterization of admissible functions on digraphs.
有向图上允许函数的类散度表征。
- DOI:
- 发表时间:2004
- 期刊:
- 影响因子:0
- 作者:J.-M.Deshouillers;K.Kawada;T.D.Wooley;G.Oshikiri;G.Oshikiri
- 通讯作者:G.Oshikiri
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OSHIKIRI Gen-ichi其他文献
OSHIKIRI Gen-ichi的其他文献
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{{ truncateString('OSHIKIRI Gen-ichi', 18)}}的其他基金
The study of relations between topological properties and differential geometric properties of foliated structures.
研究叶状结构的拓扑性质和微分几何性质之间的关系。
- 批准号:
13640056 - 财政年份:2001
- 资助金额:
$ 2.3万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Differential Geometric Approach to Foliated Structures.
叶状结构的微分几何方法。
- 批准号:
10640055 - 财政年份:1998
- 资助金额:
$ 2.3万 - 项目类别:
Grant-in-Aid for Scientific Research (C)