SPECTRAL GEOMETRY

光谱几何

• 批准号: 09640111
• 负责人: IKEDA Akira
• 金额: $ 1.86万
• 依托单位: OKAYAMA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640111/
• 关键词: Dirac operator; Spin structure; isospectral problem; spherical space forms; spectral zeta functions; Laplacian for graphs

1. We construct some examples of Dirac isospectral lens spaces containing 17 dimensional ones. To construct Dirac isospectral lens spaces, we study the first series of Laplace 0-isospectral lens spaces given by the author. By computing the Poincare series associated to the Dirac spectrum of these lens spaces, we determine which lens spaces are Dirac isospectral or not. We also determine our Dirac isospectral lens spaces are Laplace p-isospectral or not.2. Let M be a compact connected Riemannian manifold, DELTA^p_ the Laplacian acting on the space of smooth p-forms on M.Let zeta^<p, delta>_(s) be the spectral zeta function associated to the spectrum of delta-closed p-forms. We study a zeta^<p, delta>_(s) for the standard spheres with constant curvature 1 and zeta_M(s) for a compact simply connected Riemannian symmetric spaces of rank 1. We give residues of thier spectral zeta functions explicitely which have very simple forms. Moreover we give a proof zeta^<p, delta>_<D22n+1@>D2> (s) vanises at negative integers.3, We give estimates of Green kernels and Heat kernels for infinite graphs, moreover we give an sharp estimete of Green kernels and Heat kernels for some infinite regular graphs.

1。我们构建了一些狄拉克等光谱镜头空间的示例，其中包含17个维度。为了构建狄拉克等光谱镜头空间，我们研究了作者给出的第一个Laplace 0-镜面镜头空间。通过计算与这些镜头空间的狄拉克频谱相关的庞加罗系列，我们确定哪些镜头空间是狄拉克的谱。我们还确定我们的狄拉克等光谱镜头空间是否是拉普拉斯p-镜。2。令m为紧凑的连接的riemannian歧管，delta^p_ p_ laplacian作用于m.let zeta^<p，delta> _（s）上的平滑p形式的光谱zeta zeta函数与delta封闭的pforms的光谱相关的光谱zeta函数。我们研究具有恒定曲率1和Zeta_m（s）的标准球的zeta^<p，delta> _（s），对于紧凑型，简单地连接的riemannian对称空间。此外，我们给出了一个证明Zeta^<p，delta> _ <d22n+1@> d2>（s）在负整数下的消失。3，我们给出了无限图的绿色内核和热核的估计，此外，我们给出了一些无限常规图的绿色绿色内核和热核的尖锐估计。

项目成果

K.Mashimo & K.Tojo: "Circles in Riemannian symmetric spaces" Kodai Math.J.(to appear).

真下健

Y.Agaoka and E.Kaneda: "Local isometric imbeddings of symplectic groups" Geometriae Dedicata. Vol.71, No.1. 75-82 (1998)

Y.Agaoka 和 E.Kaneda：“辛群的局部等距嵌入”Geometriae Dedicata。

A.Katsuda and H.Urakawa: "The first eigenvalues of the discrete Dirichlet problem for graph" J.of Combinatorial Math. and Combinatorial Comp. (印刷中). (1998)

A. Katsuda 和 H. Urakawa：“图的离散狄利克雷问题的第一个特征值”J. of Combinatorial Math and Combinatorial Comp（正在出版）。

H.Urakawa: "A discrete analgue of harmonic morphisms" Harmonic Maps and Related Topics, Brest in 1997. (印刷中). (1999)

H.Urakawa：“调和态射的离散模拟”调和映射和相关主题，布雷斯特，1997 年。（出版中）。

H.Hashimoto and K.Mashimo: "On the some 3-dimensional CR-submanifolds in S^6" Nagoya Math, Journal. (発表予定).

H.Hashimoto 和 K.Mashimo：“关于 S^6 中的一些 3 维 CR 子流形”Nagoya Math，Journal（即将出版）。