Einstein metrics on compact simple Lie groups attached to standard triples
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- by Zaili Yan and Shaoqiang Deng PDF
- Trans. Amer. Math. Soc. 369 (2017), 8587-8605 Request permission
Abstract:
In this paper, we study left invariant Einstein metrics on compact simple Lie groups. We find a method to construct left invariant non-naturally reductive Einstein metrics on compact simple Lie groups from a standard triple. This result, combined with the classification of standard homogeneous Einstein manifolds, leads to a large number of new Einstein metrics on compact simple Lie groups which are not naturally reductive. In particular, we show that on the compact simple Lie groups $\mathrm {SO}(8)$ and $\mathrm {SO}(10)$, there exist Einstein metrics which are not naturally reductive. A further interesting result of this paper is that on the simple Lie groups $\mathrm {SO}(2n)$ and $\mathrm {Sp}(2n)$ there exist a large number of left invariant non-naturally reductive Einstein metrics.References
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Additional Information
- Zaili Yan
- Affiliation: Department of Mathematics, Ningbo University, Ningbo, Zhejiang Province, 315211, People’s Republic of China
- MR Author ID: 1042174
- Email: yanzaili@nbu.edu.cn
- Shaoqiang Deng
- Affiliation: School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, People’s Republic of China
- MR Author ID: 343544
- Email: dengsq@nankai.edu.cn
- Received by editor(s): October 15, 2015
- Received by editor(s) in revised form: January 27, 2016
- Published electronically: May 5, 2017
- Additional Notes: The first author was supported by NSFC (Nos. 11626134, 11401425) and K. C. Wong Magna Fund in Ningbo University.
The second author was supported by NSFC (Nos. 11671212, 51535008) of China - © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 8587-8605
- MSC (2010): Primary 53C25, 53C35, 53C30
- DOI: https://doi.org/10.1090/tran/7025
- MathSciNet review: 3710636