四元数Stiefel流形上的非线性Morse-Bott函数
Non-linear Morse-Bott functions on quaternionic Stiefel manifolds
摘要：
在Stiefel流形$X_{n,k}$中，用二次函数代替Frankel线性高度函数.我们证明了这仍然是一个Morse-Bott函数，其临界水平的结构根据$n-2k$的符号呈现二分法。临界子流形不再是Grassmannian，而是两个Grassmannian乘积的基纤维化的全空间。我们显式积分梯度流。
英文摘要：
In the Stiefel manifold $X_{n,k}$, we replace Frankel linear height function by a quadratic one. We prove this is still a Morse-Bott function, whose structure of critical levels presents a dichotomy according to the sign of $n-2k$. The critical submanifolds are no longer Grassmannians but total spaces of fibrations of basis a product of two Grassmannians. We explicitly integrate the gradient flow.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
