New non-naturally reductive Einstein metrics on SO(n)-Reference-Cited by-同舟云学术

New non-naturally reductive Einstein metrics on SO(n)

Published:2018-10 Issue:11 Volume:29 Page:1850083
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

Zhang Bo¹,Chen Huibin¹,Tan Ju²^ORCID

Affiliation:

1. School of Mathematical Science, Nankai University, Tianjin 300071, P. R. China

2. Department of Applied Mathematics, Anhui University of Technology, Maanshan 243032, P. R. China

Abstract

We obtain new invariant Einstein metrics on the compact Lie groups [Formula: see text] ([Formula: see text]) which are not naturally reductive. This is achieved by imposing certain symmetry assumptions in the set of all left-invariant metrics on [Formula: see text] and by computing the Ricci tensor for such metrics. The Einstein metrics are obtained as solutions of systems polynomial equations, which we manipulate by symbolic computations using Gröbner bases.

Funder

National Natural Science Foundation of China

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X18500830

Reference9 articles.

1. Invariant Einstein Metrics on Some Homogeneous Spaces of Classical Lie Groups

2. Einstein metrics on compact Lie groups which are not naturally reductive

3. New Einstein metrics on the Lie group $\mathrm{SO}(n)$ which are not naturally reductive

4. Non-naturally reductive Einstein metrics on the compact simple Lie group $$F_4$$ F 4

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