Spectral isolation of naturally reductive metrics on simple Lie groups

被引：6

作者：

Gordon, Carolyn S. ^{[1
]}

Sutton, Craig J. ^{[1
]}

机构：

[1] Dartmouth Coll, Dept Math, Hanover, NH 03755 USA

来源：

MATHEMATISCHE ZEITSCHRIFT | 2010年 / 266卷 / 04期

基金：

美国国家科学基金会;

关键词：

Laplacian; Eigenvalue spectrum; Naturally reductive metrics; Symmetric spaces; FLAT TORI; MANIFOLDS; RIGIDITY; EIGENVALUE; LAPLACIAN;

D O I：

10.1007/s00209-009-0640-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that within the class of left-invariant naturally reductive metrics M(Nat)(G) on a compact simple Lie group G, every metric is spectrally isolated. We also observe that any collection of isospectral compact symmetric spaces is finite; this follows from a somewhat stronger statement involving only a finite part of the spectrum.

引用

页码：979 / 995

页数：17

共 33 条

[21] Left invariant Randers metrics of Berwald type on tangent Lie groups
Asgari, Farhad
Moghaddam, Hamid Reza Salimi
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2018, 15 (01)
[22] Geodesics and Curvatures of Special Sub-Riemannian Metrics on Lie Groups
Berestovskii, V. N.
SIBERIAN MATHEMATICAL JOURNAL, 2018, 59 (01) : 31 - 42
[23] Invariant Einstein Metrics on Some Homogeneous Spaces of Classical Lie Groups
Arvanitoyeorgos, Andreas
Dzhepko, V. V.
Nikonorov, Yu. G.
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2009, 61 (06): : 1201 - 1213
[24] The resolutions of the singular loci of the Toda lattice on the split and connected reductive Lie groups
Ikeda, Kaoru
JOURNAL OF GEOMETRY AND PHYSICS, 2020, 148
[25] Rough similarity of left-invariant Riemannian metrics on some Lie groups
Le Donne, Enrico
Pallier, Gabriel
Xie, Xiangdong
GROUPS GEOMETRY AND DYNAMICS, 2025, 19 (01) : 227 - 263
[26] Compatibility of Balanced and SKT Metrics on Two-Step Solvable Lie Groups
Freibert, Marco
Swann, Andrew
TRANSFORMATION GROUPS, 2025, 30 (01) : 235 - 265
[27] Gromov Rigidity of Bi-Invariant Metrics on Lie Groups and Homogeneous Spaces
Sun, Yukai
Dai, Xianzhe
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2020, 16
[28] Diameter and Laplace Eigenvalue Estimates for Left-invariant Metrics on Compact Lie Groups
Lauret, Emilio A.
POTENTIAL ANALYSIS, 2023, 58 (01) : 37 - 70
[29] LEFT INVARIANT CLIFFORD-WOLF HOMOGENEOUS (α, β)-METRICS ON COMPACT SEMISIMPLE LIE GROUPS
Deng, Shaoqiang
Xu, Ming
TRANSFORMATION GROUPS, 2015, 20 (02) : 395 - 416
[30] Strong property (T) for higher-rank simple Lie groups
de Laat, Tim
de la Salle, Mikael
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2015, 111 : 936 - 966

← 1 2 3 4 →