GEOMETRY OF NUMBERS AND CODING THEORY

数字几何和编码理论

基本信息

批准号：
12640101
负责人：
UCHIDA Koji
金额：
$ 1.92万
依托单位：
Tohoku University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2001
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640101/
关键词：
Harmonic morphism of graph Discrete Laplacian Inhomogeneous Yang-Mills equation Einstein-Wey1 geometry Totally real field Lambda invariant Dehn surgery Heegaard splitting CR manifold pseudoharmonic map Yang-Mills theory Einstein-Weyl

项目摘要

Urakawa defined the harmonic morphisms of graphs, and gave good estimate of the Green kernel of an infinite tree. He found good estimate of the spectrum of the discrete Laplacian of an infinite graphs. He built Hermitian connections of a vector bundle on a CR manifold, then showed existence and uniqueness of the solution of inhomogeneous Yang-Mills equation. He proved that CR-maps of pseudo convex CR manifolds are pseudoharmonic if and only if they are pseudohermitian. He also introduced the notion of stability of the maps, and proved pseudoharmonic maps into negatively curved Riemannian manifolds are stable. He developed the Yang-Mills theory without the equation Dh=0 for connections in a vector bundle over a Riemannian manifold, and applied this theory to Einstein-Wey1 geometry and to affine differential geometry.Taya found the formula representing p-class numbers of intermediate fields of the cyclic Zpextension by the values of p-adic zeta functions, assuming Leopoldt conjecture. He also showed there exist infinitely many real quadratic fields in which the prime.3 splits such that lambda invariants are 0. He estimated the density of such fields.Shimokawa considered Dehn surgeries on strongly invertible knots yielding lens spaces. He found conditions for a graph in the disc to contain some characteristic subgraphs. He showed any Heegaard splitting of trivial arcs in a compression body is standard. He introduced the notion of Heegaard splittings of the pair (M, T), where M is a compact orientable 3-manifold and T is a 1-submanifold.

Urakawa定义了图的谐波形态，并对无限树的绿色内核进行了良好的估计。他发现了无限图的离散拉普拉斯的频谱的良好估计。他在CR歧管上建立了矢量束的Hermitian连接，然后显示出不均匀的Yang-Mills方程解决方案的存在和独特性。他证明了伪凸cr歧管的Cr映射是伪harmonic的，并且仅当它们是伪hermitian时。他还引入了地图的稳定性概念，并证明了伪harmonic地图为负弯曲的riemannian歧管稳定。 He developed the Yang-Mills theory without the equation Dh=0 for connections in a vector bundle over a Riemannian manifold, and applied this theory to Einstein-Wey1 geometry and to affine differential geometry.Taya found the formula representing p-class numbers of intermediate fields of the cyclic Zpextension by the values of p-adic zeta functions, assuming Leopoldt conjecture.他还表明，存在无限的许多二次场，其中素数为3分裂，使得lambda不变性为0。他发现光盘中图的条件包含一些特征子图。他显示了压缩体中琐碎弧的任何heegaard分裂是标准的。他介绍了这对Heegaard分裂的概念（M，T），其中M是一个可定向的3个manifold，T是1- submanifold。