Abstract
In this paper, we study G-g.o. metrics on a class of compact homogeneous spaces G/H constructed from homogeneous spaces \(G/(H\times K)\) with K a compact Lie subgroup of G. G/H can be viewed as a total space over \(G/(H\times K)\) with a fiber K. We establish the relation between G-g.o. metrics on G/H and G-g.o. metrics on \(G/(H\times K)\). Furthermore, we provide a method to determine G-g.o. metrics on G/H based on the classification of G-g.o. metrics on \(G/(H\times K)\). We also consider \(G\times H\)-invariant g.o. metrics on compact simple Lie groups arising from the derived homogeneous spaces G/H. As an application, based on the classification of compact strongly isotropy irreducible spaces \(G/(H\times K)\), we give a complete classification of G-g.o. metrics on derived homogeneous spaces G/H and prove that all \(G\times H\)-invariant g.o. metrics on compact simple Lie groups G arising from G/H are naturally reductive with respect to \(G\times H\).
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Acknowledgements
This work was partially supported by the National Natural Science Foundation of China (11571182, 11901300, 11931009, and 12131012), the Fundamental Research Fund for the Provincial Universities of Zhejiang, K.C. Wong Magna Fund in Ningbo University and the Starting research funds of Nanjing Normal University (No. 184080H202B196). The first author would like to thank Prof. Yurii Nikonorov and Prof. Yury Nikolayevsky for their helpful discussion at Chern Institute of Mathematics (Tianjin, China). The authors would like to thank the referee for helpful suggestions.
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Chen, H., Chen, Z., Yan, Z. et al. Invariant geodesic orbit metrics on certain compact homogeneous spaces. manuscripta math. 172, 651–668 (2023). https://doi.org/10.1007/s00229-022-01416-9
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DOI: https://doi.org/10.1007/s00229-022-01416-9