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

中文翻译：

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Stiefel 流形上的新不变爱因斯坦-兰德斯度量$$V_{2p}\mathbb {R}^n={\mathrm {S}}{\mathrm O}(n)/ {\mathrm {S}}{\mathrm O } (n-2p)$$

在本文中，我们考虑在 $$\mathbb {R}^n$$ R 中所有标准正交 k 帧的 Stiefel 流形 $$V_k\mathbb {R}^n$$ V k R n 上的不变爱因斯坦-兰德斯度量n ，其微分于齐次空间 $${\mathrm {S}}{\mathrm O}(n)/{\mathrm {S}}{\mathrm O}(nk)$$ SO ( n ) / SO (n-k)。我们证明对于 $$2\le p\le \frac{2}{5}n-1$$ 2 ≤ p ≤ 2 5 n - 1 ，