The Lie group of isometries of a pseudo-Riemannian manifold

被引：0

作者：

Pham, Hung ^{[1
]}

机构：

[1] Victoria Univ Wellington, Sch Math & Stat, Wellington 6140, New Zealand

来源：

ANNALS OF MATHEMATICAL SCIENCES AND APPLICATIONS | 2023年 / 8卷 / 02期

关键词：

Lie group; locally compact group; isometries; pseudo-Riemannian manifold; integral manifold;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give an elementary proof of the Myers-Steenrod theorem, stat-ing that the group of isometries of a connected Riemannian man-ifold M is a Lie group acting smoothly on M. Our proof follows the approach of Chu and Kobayashi, but replacing their use of a theorem of Palais with a topological condition detecting when a locally compact subspace of M is an embedded integral manifold of a given k-plane distribution.

引用

页码：223 / 238

页数：16

共 50 条

[11] REMARKS ON GROUP OF ISOMETRIES OF A RIEMANNIAN MANIFOLD
YAU, ST
TOPOLOGY, 1977, 16 (03) : 239 - 247
[12] Relativistic diffusion with friction on a pseudo-Riemannian manifold
Haba, Z.
CLASSICAL AND QUANTUM GRAVITY, 2010, 27 (09)
[13] On the Geometry of the Null Tangent Bundle of a Pseudo-Riemannian Manifold
Abbassi, Mohamed Tahar Kadaoui
Boulagouaz, Khadija
Calvaruso, Giovanni
AXIOMS, 2023, 12 (10)
[14] Asymptotics of the D'Alembertian with potential on a pseudo-Riemannian manifold
Branson, T
Olafsson, G
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 127 (05) : 1339 - 1345
[15] PSEUDO-RIEMANNIAN MANIFOLD OF MIXMASTER DYNAMIC-SYSTEMS
SZYDLOWSKI, M
LAPETA, A
PHYSICS LETTERS A, 1990, 148 (05) : 239 - 245
[16] Wick-rotations of pseudo-Riemannian Lie groups
Helleland, Christer
JOURNAL OF GEOMETRY AND PHYSICS, 2020, 158
[17] ON ISOMETRY GROUPS OF PSEUDO-RIEMANNIAN COMPACT LIE GROUPS
Zhu, Fuhai
Chen, Zhiqi
Liang, Ke
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2021, 149 (09) : 3991 - 3997
[18] On a remarkable class of flat pseudo-Riemannian Lie groups
Lebzioui, Hicham
JOURNAL OF GEOMETRY AND PHYSICS, 2023, 186
[19] IFHP TRANSFORMATIONS ON THE TANGENT BUNDLE OF A RIEMANNIAN MANIFOLD WITH A CLASS OF PSEUDO-RIEMANNIAN METRICS
Zohrehvand, Mosayeb
COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES, 2020, 73 (02): : 170 - 178
[20] Structure of the Projective Group in A Pseudo-Riemannian Space
Z. Kh. Zakirova
Theoretical and Mathematical Physics, 2018, 196 : 965 - 975

← 1 2 3 4 5 →