Abstract
In this paper, we study Einstein-like metrics on compact homogeneous spaces G/H. In the beginning, we give a characterization of Einstein-like metrics on compact homogeneous spaces. As an application, we classify all invariant Einstein-like metrics on compact homogeneous spaces with two isotropy summands and generalized Wallach spaces of exceptional type.
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Acknowledgements
This work was partially supported by the Natural Science Research of Jiangsu Education Institutions of China (No. 23KJB110016), Guangdong Basic and Applied Basic Research Foundation (Grant No. 2023A1515010001), and the National Natural Science Foundation of China (11931009, 11901300 and 12131012). The authors would like to thank Prof. Fuhai Zhu for the useful discussions. It is a pleasure to thank our referee for the helpful comments.
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Li, F., Chen, H. & Chen, Z. Einstein-like metrics on compact homogeneous spaces. manuscripta math. 174, 505–516 (2024). https://doi.org/10.1007/s00229-023-01508-0
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DOI: https://doi.org/10.1007/s00229-023-01508-0