Left-Invariant Pseudo-Einstein Metrics on Lie Groups

DOI

10.1142/S1402925112500155How to use a DOI?

Keywords

Pseudo-Riemannian metric; pseudo-Einstein metric; Levi-civita connection; Ricci curvature

Abstract

In this article, we focus on left-invariant pseudo-Einstein metrics on Lie groups. To begin with, we give some examples of pseudo-Einstein metrics on Lie groups. Also we calculate the Levi-civita connection, and then Ricci tensor associated with left-invariant pseudo-Riemannian metrics on the unimodular Lie groups of dimension three. Furthermore, we show that the left-invariant pseudo-Einstein metric on SL(2) is unique up to a constant. At last, we study the left-invariant pseudo-Riemannian metrics on compact Lie groups and classify the pseudo-Einstein metrics on the low-dimensional compact Lie groups.

Copyright

© 2012 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Sheng Chen
AU  - Ke Liang
PY  - 2012
DA  - 2012/07/04
TI  - Left-Invariant Pseudo-Einstein Metrics on Lie Groups
JO  - Journal of Nonlinear Mathematical Physics
SP  - 236
EP  - 246
VL  - 19
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925112500155
DO  - 10.1142/S1402925112500155
ID  - Chen2012
ER  -