标题： 四元数丛在某些流形上的射影空间的双商模型 显示英文标题

标题： The biquotient model of the total space of the projectivization quaternionic bundles over certain manifolds

摘要： 在本文中，我们计算从四元数切向量丛$\tau: \mathbb{H}^{n} \rightarrow E \rightarrow M$在四元数流形$M$上得到的四元数射影丛$P(\tau): \mathbb{H}P^{n-1} \rightarrow P(E) \rightarrow M$的有理同伦类型。 如果基空间$M$是四元数射影空间$\mathbb{H}P^{2}$，那么四元数射影丛$P(\tau)$的全空间$P(E)$的有理同伦类型由一个双商模型$Sp(1)\backslash Sp(3) / Sp(1) \times Sp(1)$给出。 显示英文摘要

摘要： In this paper, we compute the rational homotopy type of the quaternionic projective bundle $P(\tau): \mathbb{H}P^{n-1} \rightarrow P(E) \rightarrow M$ obtain from the quaternionic tangent bundle $\tau: \mathbb{H}^{n} \rightarrow E \rightarrow M$ over quaternionic manifold $M$. If the base space $M$ is the quaternionic projective space $\mathbb{H}P^{2}$, then the rational homotopy type of the total space $P(E)$ of the quaternionic projective bundle $P(\tau)$ is given by a biquotient model $Sp(1)\backslash Sp(3) / Sp(1) \times Sp(1)$.