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New Invariant Einstein–Randers Metrics on Stiefel Manifolds\(V_{2p}\mathbb {R}^n={\mathrm {S}}{\mathrm O}(n)/ {\mathrm {S}}{\mathrm O} (n-2p)\)

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Abstract

In this paper, we consider invariant Einstein–Randers metrics on the Stiefel manifolds \(V_k\mathbb {R}^n\) of all orthonormal k-frames in \(\mathbb {R}^n\), which is diffeomorphic to the homogeneous space \({\mathrm {S}}{\mathrm O}(n)/{\mathrm {S}}{\mathrm O}(n-k)\). We prove that for \(2\le p\le \frac{2}{5}n-1\), there are four different families of \({\mathrm {S}}{\mathrm O}(n)\)-invariant Einstein–Randers metrics on \({\mathrm {S}}{\mathrm O}(n)/{\mathrm {S}}{\mathrm O}(n-2p)\) whose corresponding Riemannian metrics are determined by \({\mathrm {A}}{\mathrm {d}}(U(p)\times {\mathrm {S}}{\mathrm O}(n-2p))\)-invariant inner products on the tangent space of \({\mathrm {S}}{\mathrm O}(n)/{\mathrm {S}}{\mathrm O}(n-2p)\).

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Acknowledgements

The authors want to express their sincere thanks to the referees for their valuable remarks and suggestions, which made this paper more readable. This work is supported in part by National Natural Science Foundation of China (Nos. 11571182, 11901300 and 11931009) and Natural Science Research of Jiangsu Education Institutions of China (No. 19KJB110015).

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Authors and Affiliations

  1. School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, People’s Republic of China

    Huibin Chen

  2. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, People’s Republic of China

    Chao Chen & Zhiqi Chen

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  1. Huibin Chen
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  2. Chao Chen
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  3. Zhiqi Chen
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Correspondence to Chao Chen.

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Chen, H., Chen, C. & Chen, Z. New Invariant Einstein–Randers Metrics on Stiefel Manifolds\(V_{2p}\mathbb {R}^n={\mathrm {S}}{\mathrm O}(n)/ {\mathrm {S}}{\mathrm O} (n-2p)\). Results Math 76, 19 (2021). https://doi.org/10.1007/s00025-020-01333-x

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