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| New Homogeneous Einstein Metrics on SO(7)/T |
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Citation： |
Yu WANG,Tianzeng LI,Guosong ZHAO.New Homogeneous Einstein Metrics on SO(7)/T[J].Chinese Annals of Mathematics B,2018,39(1):97~110 |
| Page view： 1894
Net amount： 2041 |
Authors： |
Yu WANG; Tianzeng LI;Guosong ZHAO |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11501390, 61573010), the Fund of Sichuan
University of Science and Engineering (No.2015RC10), the Opening
Project of Sichuan Province University Key Laboratory of Bridge
Non-destruction Detecting and Engineering Computing (No.2014QZJ03)
and the Opening Project of Key Laboratory of Higher Education of
Sichuan Province for Enterprise Informationalization and Internet of
Things (No.2016WYJ04). |
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| Abstract： |
The authors compute non-zero structure constants of the full flag
manifold $M={\rm SO}(7)/T$ with nine isotropy summands, then
construct the Einstein equations. With the help of computer they get
all the forty-eight positive solutions (up to a scale ) for ${\rm
SO}(7)/T$, up to isometry there are only five $G$-invariant Einstein
metrics, of which one is K\"ahler Einstein metric and four are
non-K\"ahler Einstein metrics. |
Keywords： |
Generalized flag manifold, Einstein metric, Ricci tensor, Isotropyrepresentation, Isometry |
Classification： |
53C30, 17B22 |
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