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

[1] Spectral isolation of naturally reductive metrics on simple Lie groups
Carolyn S. Gordon
Craig J. Sutton
Mathematische Zeitschrift, 2010, 266 : 979 - 995
[2] SPECTRAL ISOLATION OF BI-INVARIANT METRICS ON COMPACT LIE GROUPS
Gordon, Carolyn S.
Schueth, Dorothee
Sutton, Craig J.
ANNALES DE L INSTITUT FOURIER, 2010, 60 (05) : 1617 - 1628
[3] Einstein metrics on compact Lie groups which are not naturally reductive
Arvanitoyeorgos, Andreas
Mori, Kunihiko
Sakane, Yusuke
GEOMETRIAE DEDICATA, 2012, 160 (01) : 261 - 285
[4] Einstein metrics on compact Lie groups which are not naturally reductive
Andreas Arvanitoyeorgos
Kunihiko Mori
Yusuke Sakane
Geometriae Dedicata, 2012, 160 : 261 - 285
[5] Non-naturally reductive Einstein metrics on exceptional Lie groups
Chrysikos, Ioannis
Sakane, Yusuke
JOURNAL OF GEOMETRY AND PHYSICS, 2017, 116 : 152 - 186
[6] Non-naturally reductive Einstein metrics on the compact simple Lie group
Chen, Zhiqi
Liang, Ke
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2014, 46 (02) : 103 - 115
[7] Tangent Lie Groups are Riemannian Naturally Reductive Spaces
Agricola, Ilka
Ferreira, Ana Cristina
ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2017, 27 (02) : 895 - 911
[8] EINSTEIN METRICS ON COMPACT SIMPLE LIE GROUPS ATTACHED TO STANDARD TRIPLES
Yan, Zaili
Deng, Shaoqiang
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 369 (12) : 8587 - 8605
[9] Homogeneous Einstein (α, β)-metrics on compact simple Lie groups and spheres
Yan, Zaili
Deng, Shaoqiang
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2017, 148 : 147 - 160
[10] NATURALLY REDUCTIVE PSEUDO-RIEMANNIAN 2-STEP NILPOTENT LIE GROUPS
Ovando, Gabriela P.
HOUSTON JOURNAL OF MATHEMATICS, 2013, 39 (01): : 147 - 167

← 1 2 3 4 →