Non-naturally reductive Einstein metrics on Sp(<i>n</i>)

doi:10.1007/s11464-020-0818-0

Front. Math. China

2020, Vol. 15

Issue (1) : 47-55 https://doi.org/10.1007/s11464-020-0818-0

RESEARCH ARTICLE

Non-naturally reductive Einstein metrics on Sp(n)

Zhiqi CHEN¹, Huibin CHEN²(

)

¹. School of Mathematical Sciences, Nankai University, Tianjin 300071, China
². School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China

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Abstract

We prove that Sp(2k+l) admits at least two non-naturally reductive Einstein metrics which are Ad(Sp(k)×Sp(k)×Sp(l))-invariant if k<l.It implies that every compact simple Lie group Sp(n) for n≥4 admits at least 2[(n−1)/3] non-naturally reductive left-invariant Einstein metrics.

Keywords Einstein metric non-naturally reductive metric Riemannian manifold Lie group

Corresponding Author(s): Huibin CHEN

Issue Date: 09 March 2020

Cite this article:

Zhiqi CHEN,Huibin CHEN. Non-naturally reductive Einstein metrics on Sp(n)[J]. Front. Math. China, 2020, 15(1): 47-55.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-020-0818-0
https://academic.hep.com.cn/fmc/EN/Y2020/V15/I1/47

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