New Homogeneous Einstein Metrics on SO(7)/T


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
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Yu WANG; Tianzeng LI;Guosong ZHAO


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).
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.


Generalized flag manifold, Einstein metric, Ricci tensor, Isotropyrepresentation, Isometry


53C30, 17B22
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