New Homogeneous Einstein Metrics on SO(7)/T

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: 610        Net amount: 668

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).
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
Download PDF Full-Text

Organizer:The Ministry of Education of China Sponsor:Fudan University Address:220 Handan Road, Fudan University, Shanghai, China E-mail:edcam@fudan.edu.cn
Designed by Beijing E-Tiller Co.,Ltd.