New Einstein metrics on Sp ( n ) which are non-naturally reductive

Shaoxiang Zhang; Huibin Chen

Czechoslovak Mathematical Journal (2022)

  • Volume: 72, Issue: 2, page 349-363
  • ISSN: 0011-4642

Abstract

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We prove that there are at least two new non-naturally reductive Ad ( Sp ( l ) × Sp ( k ) × Sp ( k ) × Sp ( k ) ) invariant Einstein metrics on Sp ( l + 3 k ) ( k < l ) . It implies that every compact simple Lie group Sp ( n ) for n = l + 3 k > 4 admits at least 2 [ 1 4 ( n - 1 ) ] non-naturally reductive Ad ( Sp ( l ) × Sp ( k ) × Sp ( k ) × Sp ( k ) ) invariant Einstein metrics.

How to cite

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Zhang, Shaoxiang, and Chen, Huibin. "New Einstein metrics on ${\rm Sp}(n)$ which are non-naturally reductive." Czechoslovak Mathematical Journal 72.2 (2022): 349-363. <http://eudml.org/doc/298312>.

@article{Zhang2022,
abstract = {We prove that there are at least two new non-naturally reductive $\{\rm Ad\}(\{\rm Sp\}(l)\times \{\rm Sp\}(k)\times \{\rm Sp\}(k)\times \{\rm Sp\}(k))$ invariant Einstein metrics on $\{\rm Sp\} (l+3k)$$(k < l)$. It implies that every compact simple Lie group $\{\rm Sp\} (n)$ for $n= l+3k>4$ admits at least $2[\tfrac\{1\}\{4\} (n-1)]$ non-naturally reductive $\{\rm Ad\}(\{\rm Sp\}(l)\times \{\rm Sp\}(k)\times \{\rm Sp\}(k)\times \{\rm Sp\}(k))$ invariant Einstein metrics.},
author = {Zhang, Shaoxiang, Chen, Huibin},
journal = {Czechoslovak Mathematical Journal},
keywords = {Einstein metric; non-naturally reductive metric; compact Lie group; symplectic group},
language = {eng},
number = {2},
pages = {349-363},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {New Einstein metrics on $\{\rm Sp\}(n)$ which are non-naturally reductive},
url = {http://eudml.org/doc/298312},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Zhang, Shaoxiang
AU - Chen, Huibin
TI - New Einstein metrics on ${\rm Sp}(n)$ which are non-naturally reductive
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 2
SP - 349
EP - 363
AB - We prove that there are at least two new non-naturally reductive ${\rm Ad}({\rm Sp}(l)\times {\rm Sp}(k)\times {\rm Sp}(k)\times {\rm Sp}(k))$ invariant Einstein metrics on ${\rm Sp} (l+3k)$$(k < l)$. It implies that every compact simple Lie group ${\rm Sp} (n)$ for $n= l+3k>4$ admits at least $2[\tfrac{1}{4} (n-1)]$ non-naturally reductive ${\rm Ad}({\rm Sp}(l)\times {\rm Sp}(k)\times {\rm Sp}(k)\times {\rm Sp}(k))$ invariant Einstein metrics.
LA - eng
KW - Einstein metric; non-naturally reductive metric; compact Lie group; symplectic group
UR - http://eudml.org/doc/298312
ER -

References

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