Abstract
In this paper, we consider a class of left invariant Riemannian metrics on Sp(n), which is invariant under the adjoint action of the subgroup Sp(n − 3) × Sp(1) × Sp(1) × Sp(1). Based on the related formulae in the literature, we show that the existence of Einstein metrics is equivalent to the existence of solutions of some homogeneous Einstein equations. Then we use a technique of the Gröbner basis to get a sufficient condition for the existence, and show that this method will lead to new non-naturally reductive metrics.
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This work was supported by NSFC (12071228, 11901300, 51535008) and Natural Science Research of Jiangsu Education Institutions of China (19KJB110015).
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Zhang, S., Chen, H. & Deng, S. New Non-Naturally Reductive Einstein Metrics on Sp(n). Acta Math Sci 41, 887–898 (2021). https://doi.org/10.1007/s10473-021-0315-x
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DOI: https://doi.org/10.1007/s10473-021-0315-x